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Code Number

Find square root of quadratic equation

The given problem involves finding the square roots of a quadratic equation in the form ax^2 + bx + c = 0, where 'a', 'b', and 'c' are the coefficients of the quadratic equation and 'x' represents the unknown variable.

Problem Statement

The task is to write a program that calculates the square roots of a given quadratic equation and displays the results. The program should handle three different cases based on the discriminant of the equation.

Explanation with Suitable Example

Let's consider the quadratic equation: 4x^2 + 8x + 4 = 0

Here, 'a' is 4, 'b' is 8, and 'c' is 4.

Standard Pseudocode

1. Start
2. Read coefficients a, b, and c
3. Calculate discriminant (D) = b^2 - 4ac
4. If D == 0, then
    4.1 Calculate the single root r = -b / 2a
    4.2 Print "The quadratic equation has a single real root: r"
5. Else if D > 0, then
    5.1 Calculate two distinct real roots r1 = (-b + sqrt(D)) / 2a and r2 = (-b - sqrt(D)) / 2a
    5.2 Print "The quadratic equation has two distinct real roots: r1 and r2"
6. Else (D < 0), then
    6.1 Calculate real part r = -b / 2a and imaginary part i = sqrt(-D) / 2a
    6.2 Print "The quadratic equation has two distinct complex roots: r + i and r - i"
7. End

Algorithm with Proper Explanation

  1. Start the program and define the squareRoot function that takes three arguments 'a', 'b', and 'c'.

  2. Calculate the discriminant (D) using the formula discriminant = (b * b) - (4 * a * c).

  3. Based on the value of the discriminant, follow these conditions:

    • If the discriminant is zero, calculate the single root using r1 = (-b) / (2 * a) and set r2 to the same value. This indicates two identical real roots.
    • If the discriminant is positive, calculate two distinct real roots using the formulas r1 = ((-b) + sqrt(discriminant)) / (2 * a) and r2 = ((-b) - sqrt(discriminant)) / (2 * a).
    • If the discriminant is negative, calculate the real and imaginary parts separately. The real part is r = (-b) / (2 * a) and the imaginary part is imaginary = sqrt(-discriminant) / (2 * a).

  4. Print the results for each case accordingly.

  5. In the main function, call the squareRoot function for three different quadratic equations.

Code Solution

Here given code implementation process.

//  C program 
//  Find square root of quadratic equation
#include <stdio.h>
#include <math.h>

void squareRoot(float a, float b, float c)
{
  
    // Quadratic formula
    /*            _______
            −b ± √b2−4ac
        x = ————————————
                2a
    */
    // Calculate polynomial with an order of 2
    // ax²+bx+c = 0
    
    float discriminant = (b * b) - (4 * a * c);
    
    float r1 = 0.0;
    float r2 = 0.0;

    // Display parameter
    printf("\n Given a : %f",a);
    printf("\n Given b : %f",b);
    printf("\n Given c : %f",c);

    if(discriminant == 0)
    {
        // When (b²−4ac) == 0

        r1 = (-b) / (2 * a);

        r2 = r1;


        // Print two equal and real roots
        printf("\n X =  %f ",r1);
        printf("\n X =  %f ",r2);
    }
    else
    {

        if(discriminant > 0)
        {
            // When (b²−4ac) > 0

            r1 = ((-b) + sqrt(discriminant)) / (2 * a);
            r2 = ((-b) - sqrt(discriminant)) / (2 * a);

            // Print two distinct and real roots
            printf("\n X =  %f ",r1);
            printf("\n X =  %f ",r2);
        }
        else
        {
            // (b²−4ac) < 0 

            float imaginary = sqrt(-discriminant) / (2 * a);

            r1 = (-b) / (2 * a);
            r2 = r1;
            // Print two distinct complex roots 
            printf("\n X =  %f + %fi ",r1, imaginary);
            printf("\n X =  %f - %fi ",r2, imaginary);
        }
    }
    printf("\n");
}
int main(int argc, char
    const *argv[])
{


    // Case A
    // 4x²+8x+4 = 0
    // a = 4, b = 8, c = 4
    squareRoot(4, 8, 4);


    // Case B
    // 7x²+3x+2 = 0
    // a = 7, b = 3, c= 2
    squareRoot( 7, 3, 2);


    // Case C
    // 5x²+7x+2 = 0
    // a = 5, b = 7, c = 2
    squareRoot(5, 7, 2);
    return 0;
}

Output

 Given a : 4.000000
 Given b : 8.000000
 Given c : 4.000000
 X =  -1.000000
 X =  -1.000000

 Given a : 7.000000
 Given b : 3.000000
 Given c : 2.000000
 X =  -0.214286 + 0.489690i
 X =  -0.214286 - 0.489690i

 Given a : 5.000000
 Given b : 7.000000
 Given c : 2.000000
 X =  -0.400000
 X =  -1.000000
/*
  Java program
  Find square root of quadratic equation
*/
public class QuadraticEquation
{
    public void squareRoot(double a, double b, double c)
    {
        // Quadratic formula
        //            _______
        //      −b ± √b2−4ac
        //  x = ————————————
        //          2a
        //
        // Calculate polynomial with an order of 2
        // ax²+bx+c = 0
        double discriminant = (b * b) - (4 * a * c);
        double r1 = 0.0;
        double r2 = 0.0;
        // Display parameter
        System.out.print("\n Given a : " + a );
        System.out.print("\n Given b : " + b );
        System.out.print("\n Given c : " + c );
        if (discriminant == 0)
        {
            // When (b²−4ac) == 0
            r1 = (-b) / (2 * a);
            r2 = r1;
            // Print two equal and real roots
            System.out.print("\n X = " + r1 );
            System.out.print("\n X = " + r2 );
        }
        else
        {
            if (discriminant > 0)
            {
                // When (b²−4ac) > 0
                r1 = ((-b) + Math.sqrt(discriminant)) / (2 * a);
                r2 = ((-b) - Math.sqrt(discriminant)) / (2 * a);
                // Print two distinct and real roots
                System.out.print("\n X = " + r1 );
                System.out.print("\n X = " + r2 );
            }
            else
            {
                // (b²−4ac) < 0 
                double imaginary = Math.sqrt(-discriminant) / (2 * a);
                r1 = (-b) / (2 * a);
                r2 = r1;
                // Print two distinct complex roots 
                System.out.print("\n X = " + r1 + " + " + imaginary + "i ");
                System.out.print("\n X = " + r2 + " - " + imaginary + "i ");
            }
        }
        System.out.print("\n");
    }
    public static void main(String[] args)
    {
        QuadraticEquation task = new QuadraticEquation();


        // Case A
        // 4x²+8x+4 = 0
        // a = 4, b = 8, c = 4
        task.squareRoot(4, 8, 4);


        // Case B
        // 7x²+3x+2 = 0
        // a = 7, b = 3, c= 2
        task.squareRoot( 7, 3, 2);


        // Case C
        // 5x²+7x+2 = 0
        // a = 5, b = 7, c = 2
        task.squareRoot(5, 7, 2);
       
    }
}

Output

 Given a : 4.0
 Given b : 8.0
 Given c : 4.0
 X = -1.0
 X = -1.0

 Given a : 7.0
 Given b : 3.0
 Given c : 2.0
 X = -0.21428571428571427 + 0.48968961431436026i
 X = -0.21428571428571427 - 0.48968961431436026i

 Given a : 5.0
 Given b : 7.0
 Given c : 2.0
 X = -0.4
 X = -1.0
// Include header file
#include <iostream>
#include <math.h>
using namespace std;
/*
  C++ program
  Find square root of quadratic equation
*/
class QuadraticEquation
{
	public: void squareRoot(double a, double b, double c)
	{
		// Quadratic formula
		//            _______
		//      −b ± √b2−4ac
		//  x = ————————————
		//          2a
		//
		// Calculate polynomial with an order of 2
		// ax²+bx+c = 0
		double discriminant = (b *b) - (4 *a *c);
		double r1 = 0.0;
		double r2 = 0.0;
		// Display parameter
		cout << "\n Given a : " << a;
		cout << "\n Given b : " << b;
		cout << "\n Given c : " << c;
		if (discriminant == 0)
		{
			// When (b²−4ac) == 0
			r1 = (-b) / (2 *a);
			r2 = r1;
			// Print two equal and real roots
			cout << "\n X = " << r1;
			cout << "\n X = " << r2;
		}
		else
		{
			if (discriminant > 0)
			{
				// When (b²−4ac) > 0
				r1 = ((-b) + sqrt(discriminant)) / (2 *a);
				r2 = ((-b) - sqrt(discriminant)) / (2 *a);
				// Print two distinct and real roots
				cout << "\n X = " << r1;
				cout << "\n X = " << r2;
			}
			else
			{
				// (b²−4ac) < 0
				double imaginary = sqrt(-discriminant) / (2 *a);
				r1 = (-b) / (2 *a);
				r2 = r1;
				// Print two distinct complex roots
				cout << "\n X = " << r1 << " + " << imaginary << "i ";
				cout << "\n X = " << r2 << " - " << imaginary << "i ";
			}
		}
		cout << "\n";
	}
};
int main()
{
	QuadraticEquation task = QuadraticEquation();
	// Case A
	// 4x²+8x+4 = 0
	// a = 4, b = 8, c = 4
	task.squareRoot(4, 8, 4);
	// Case B
	// 7x²+3x+2 = 0
	// a = 7, b = 3, c= 2
	task.squareRoot(7, 3, 2);
	// Case C
	// 5x²+7x+2 = 0
	// a = 5, b = 7, c = 2
	task.squareRoot(5, 7, 2);
	return 0;
}

Output

 Given a : 4
 Given b : 8
 Given c : 4
 X = -1
 X = -1

 Given a : 7
 Given b : 3
 Given c : 2
 X = -0.214286 + 0.48969i
 X = -0.214286 - 0.48969i

 Given a : 5
 Given b : 7
 Given c : 2
 X = -0.4
 X = -1
// Include namespace system
using System;
using System.Collections.Generic;
/*
  C# program
  Find square root of quadratic equation
*/
public class QuadraticEquation
{
	public void squareRoot(double a, double b, double c)
	{
		// Quadratic formula
		//            _______
		//      −b ± √b2−4ac
		//  x = ————————————
		//          2a
		//
		// Calculate polynomial with an order of 2
		// ax²+bx+c = 0
		double discriminant = (b * b) - (4 * a * c);
		double r1 = 0.0;
		double r2 = 0.0;
		// Display parameter
		Console.Write("\n Given a : " + a);
		Console.Write("\n Given b : " + b);
		Console.Write("\n Given c : " + c);
		if (discriminant == 0)
		{
			// When (b²−4ac) == 0
			r1 = (-b) / (2 * a);
			r2 = r1;
			// Print two equal and real roots
			Console.Write("\n X = " + r1);
			Console.Write("\n X = " + r2);
		}
		else
		{
			if (discriminant > 0)
			{
				// When (b²−4ac) > 0
				r1 = ((-b) + Math.Sqrt(discriminant)) / (2 * a);
				r2 = ((-b) - Math.Sqrt(discriminant)) / (2 * a);
				// Print two distinct and real roots
				Console.Write("\n X = " + r1);
				Console.Write("\n X = " + r2);
			}
			else
			{
				// (b²−4ac) < 0
				double imaginary = Math.Sqrt(-discriminant) / (2 * a);
				r1 = (-b) / (2 * a);
				r2 = r1;
				// Print two distinct complex roots
				Console.Write("\n X = " + r1 + " + " + imaginary + "i ");
				Console.Write("\n X = " + r2 + " - " + imaginary + "i ");
			}
		}
		Console.Write("\n");
	}
	public static void Main(String[] args)
	{
		QuadraticEquation task = new QuadraticEquation();
		// Case A
		// 4x²+8x+4 = 0
		// a = 4, b = 8, c = 4
		task.squareRoot(4, 8, 4);
		// Case B
		// 7x²+3x+2 = 0
		// a = 7, b = 3, c= 2
		task.squareRoot(7, 3, 2);
		// Case C
		// 5x²+7x+2 = 0
		// a = 5, b = 7, c = 2
		task.squareRoot(5, 7, 2);
	}
}

Output

 Given a : 4
 Given b : 8
 Given c : 4
 X = -1
 X = -1

 Given a : 7
 Given b : 3
 Given c : 2
 X = -0.214285714285714 + 0.48968961431436i
 X = -0.214285714285714 - 0.48968961431436i

 Given a : 5
 Given b : 7
 Given c : 2
 X = -0.4
 X = -1
<?php
/*
  Php program
  Find square root of quadratic equation
*/
class QuadraticEquation
{
	public	function squareRoot($a, $b, $c)
	{
		// Quadratic formula
		//            _______
		//      −b ± √b2−4ac
		//  x = ————————————
		//          2a
		//
		// Calculate polynomial with an order of 2
		// ax²+bx+c = 0
		$discriminant = ($b * $b) - (4 * $a * $c);
		$r1 = 0.0;
		$r2 = 0.0;
		// Display parameter
		echo "\n Given a : ". $a;
		echo "\n Given b : ". $b;
		echo "\n Given c : ". $c;
		if ($discriminant == 0)
		{
			// When (b²−4ac) == 0
			$r1 = ((-$b) / (2 * $a));
			$r2 = $r1;
			// Print two equal and real roots
			echo "\n X = ". $r1;
			echo "\n X = ". $r2;
		}
		else
		{
			if ($discriminant > 0)
			{
				// When (b²−4ac) > 0
				$r1 = (((-$b) + sqrt($discriminant)) / (2 * $a));
				$r2 = (((-$b) - sqrt($discriminant)) / (2 * $a));
				// Print two distinct and real roots
				echo "\n X = ". $r1;
				echo "\n X = ". $r2;
			}
			else
			{
				// (b²−4ac) < 0
				$imaginary = (sqrt(-$discriminant) / (2 * $a));
				$r1 = ((-$b) / (2 * $a));
				$r2 = $r1;
				// Print two distinct complex roots
				echo "\n X = ". $r1 ." + ". $imaginary ."i ";
				echo "\n X = ". $r2 ." - ". $imaginary ."i ";
			}
		}
		echo "\n";
	}
}

function main()
{
	$task = new QuadraticEquation();
	// Case A
	// 4x²+8x+4 = 0
	// a = 4, b = 8, c = 4
	$task->squareRoot(4, 8, 4);
	// Case B
	// 7x²+3x+2 = 0
	// a = 7, b = 3, c= 2
	$task->squareRoot(7, 3, 2);
	// Case C
	// 5x²+7x+2 = 0
	// a = 5, b = 7, c = 2
	$task->squareRoot(5, 7, 2);
}
main();

Output

 Given a : 4
 Given b : 8
 Given c : 4
 X = -1
 X = -1

 Given a : 7
 Given b : 3
 Given c : 2
 X = -0.21428571428571 + 0.48968961431436i
 X = -0.21428571428571 - 0.48968961431436i

 Given a : 5
 Given b : 7
 Given c : 2
 X = -0.4
 X = -1
/*
  Node Js program
  Find square root of quadratic equation
*/
class QuadraticEquation
{
	squareRoot(a, b, c)
	{
		// Quadratic formula
		//            _______
		//      −b ± √b2−4ac
		//  x = ————————————
		//          2a
		//
		// Calculate polynomial with an order of 2
		// ax²+bx+c = 0
		var discriminant = (b * b) - (4 * a * c);
		var r1 = 0.0;
		var r2 = 0.0;
		// Display parameter
		process.stdout.write("\n Given a : " + a);
		process.stdout.write("\n Given b : " + b);
		process.stdout.write("\n Given c : " + c);
		if (discriminant == 0)
		{
			// When (b²−4ac) == 0
			r1 = ((-b) / (2 * a));
			r2 = r1;
			// Print two equal and real roots
			process.stdout.write("\n X = " + r1);
			process.stdout.write("\n X = " + r2);
		}
		else
		{
			if (discriminant > 0)
			{
				// When (b²−4ac) > 0
				r1 = ((-b) + Math.sqrt(discriminant)) / (2 * a);
				r2 = ((-b) - Math.sqrt(discriminant)) / (2 * a);
				// Print two distinct and real roots
				process.stdout.write("\n X = " + r1);
				process.stdout.write("\n X = " + r2);
			}
			else
			{
				// (b²−4ac) < 0
				var imaginary = (Math.sqrt(-discriminant) / (2 * a));
				r1 = ((-b) / (2 * a));
				r2 = r1;
				// Print two distinct complex roots
				process.stdout.write("\n X = " + r1 + " + " + imaginary + "i ");
				process.stdout.write("\n X = " + r2 + " - " + imaginary + "i ");
			}
		}
		process.stdout.write("\n");
	}
}

function main()
{
	var task = new QuadraticEquation();
	// Case A
	// 4x²+8x+4 = 0
	// a = 4, b = 8, c = 4
	task.squareRoot(4, 8, 4);
	// Case B
	// 7x²+3x+2 = 0
	// a = 7, b = 3, c= 2
	task.squareRoot(7, 3, 2);
	// Case C
	// 5x²+7x+2 = 0
	// a = 5, b = 7, c = 2
	task.squareRoot(5, 7, 2);
}
main();

Output

 Given a : 4
 Given b : 8
 Given c : 4
 X = -1
 X = -1

 Given a : 7
 Given b : 3
 Given c : 2
 X = -0.21428571428571427 + 0.48968961431436026i
 X = -0.21428571428571427 - 0.48968961431436026i

 Given a : 5
 Given b : 7
 Given c : 2
 X = -0.4
 X = -1
#   Ruby program
#   Find square root of quadratic equation

class QuadraticEquation 
	def squareRoot(a, b, c) 
		#  Quadratic formula
		#             _______
		#       −b ± √b2−4ac
		#   x = ————————————
		#           2a
		# 
		#  Calculate polynomial with an order of 2
		#  ax²+bx+c = 0
		discriminant = (b * b) - (4 * a * c)
		r1 = 0.0
		r2 = 0.0
		#  Display parameter
		print("\n Given a : ", a)
		print("\n Given b : ", b)
		print("\n Given c : ", c)
		if (discriminant == 0) 
			#  When (b²−4ac) == 0
			r1 = (-b) / (2 * a)
			r2 = r1
			#  Print two equal and real roots
			print("\n X = ", r1)
			print("\n X = ", r2)
		else 
			if (discriminant > 0) 
				#  When (b²−4ac) > 0
				r1 = ((-b) + Math.sqrt(discriminant)) / (2 * a)
				r2 = ((-b) - Math.sqrt(discriminant)) / (2 * a)
				#  Print two distinct and real roots
				print("\n X = ", r1)
				print("\n X = ", r2)
			else 
				#  (b²−4ac) < 0 
				imaginary = Math.sqrt(-discriminant) / (2 * a)
				r1 = (-b).to_f / (2 * a)
				r2 = r1
				#  Print two distinct complex roots 
				print("\n X = ", r1 ," + ", imaginary ,"i ")
				print("\n X = ", r2 ," - ", imaginary ,"i ")
			end

		end

		print("\n")
	end

end

def main() 
	task = QuadraticEquation.new()
	#  Case A
	#  4x²+8x+4 = 0
	#  a = 4, b = 8, c = 4
	task.squareRoot(4, 8, 4)
	#  Case B
	#  7x²+3x+2 = 0
	#  a = 7, b = 3, c= 2
	task.squareRoot(7, 3, 2)
	#  Case C
	#  5x²+7x+2 = 0
	#  a = 5, b = 7, c = 2
	task.squareRoot(5, 7, 2)
end

main()

Output

 Given a : 4
 Given b : 8
 Given c : 4
 X = -1
 X = -1

 Given a : 7
 Given b : 3
 Given c : 2
 X = -0.21428571428571427 + 0.48968961431436026i 
 X = -0.21428571428571427 - 0.48968961431436026i 

 Given a : 5
 Given b : 7
 Given c : 2
 X = -0.4
 X = -1.0

/*
  Scala program
  Find square root of quadratic equation
*/
class QuadraticEquation
{
	def squareRoot(a: Double, b: Double, c: Double): Unit = {
		// Quadratic formula
		//            _______
		//      −b ± √b2−4ac
		//  x = ————————————
		//          2a
		//
		// Calculate polynomial with an order of 2
		// ax²+bx+c = 0
		var discriminant: Double = (b * b) - (4 * a * c);
		var r1: Double = 0.0;
		var r2: Double = 0.0;
		// Display parameter
		print("\n Given a : " + a);
		print("\n Given b : " + b);
		print("\n Given c : " + c);
		if (discriminant == 0)
		{
			// When (b²−4ac) == 0
			r1 = ((-b) / (2 * a));
			r2 = r1;
			// Print two equal and real roots
			print("\n X = " + r1);
			print("\n X = " + r2);
		}
		else
		{
			if (discriminant > 0)
			{
				// When (b²−4ac) > 0
				r1 = (((-b) + Math.sqrt(discriminant)) / (2 * a));
				r2 = (((-b) - Math.sqrt(discriminant)) / (2 * a));
				// Print two distinct and real roots
				print("\n X = " + r1);
				print("\n X = " + r2);
			}
			else
			{
				// (b²−4ac) < 0
				var imaginary: Double = (Math.sqrt(-discriminant) / (2 * a));
				r1 = ((-b) / (2 * a));
				r2 = r1;
				// Print two distinct complex roots
				print("\n X = " + r1 + " + " + imaginary + "i ");
				print("\n X = " + r2 + " - " + imaginary + "i ");
			}
		}
		print("\n");
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: QuadraticEquation = new QuadraticEquation();
		// Case A
		// 4x²+8x+4 = 0
		// a = 4, b = 8, c = 4
		task.squareRoot(4, 8, 4);
		// Case B
		// 7x²+3x+2 = 0
		// a = 7, b = 3, c= 2
		task.squareRoot(7, 3, 2);
		// Case C
		// 5x²+7x+2 = 0
		// a = 5, b = 7, c = 2
		task.squareRoot(5, 7, 2);
	}
}

Output

 Given a : 4.0
 Given b : 8.0
 Given c : 4.0
 X = -1.0
 X = -1.0

 Given a : 7.0
 Given b : 3.0
 Given c : 2.0
 X = -0.21428571428571427 + 0.48968961431436026i
 X = -0.21428571428571427 - 0.48968961431436026i

 Given a : 5.0
 Given b : 7.0
 Given c : 2.0
 X = -0.4
 X = -1.0
import Foundation
/*
  Swift 4 program
  Find square root of quadratic equation
*/
class QuadraticEquation
{
	func squareRoot(_ a: Double, _ b: Double, _ c: Double)
	{
		// Quadratic formula
		//            _______
		//      −b ± √b2−4ac
		//  x = ————————————
		//          2a
		//
		// Calculate polynomial with an order of 2
		// ax²+bx+c = 0
		let discriminant: Double = (b * b) - (4 * a * c);
		var r1: Double = 0.0;
		var r2: Double = 0.0;
		// Display parameter
		print("\n Given a : ", a, terminator: "");
		print("\n Given b : ", b, terminator: "");
		print("\n Given c : ", c, terminator: "");
		if (discriminant == 0)
		{
			// When (b²−4ac) == 0
			r1 = (-b) / (2 * a);
			r2 = r1;
			// Print two equal and real roots
			print("\n X = ", r1, terminator: "");
			print("\n X = ", r2, terminator: "");
		}
		else
		{
			if (discriminant > 0)
			{
				// When (b²−4ac) > 0
				r1 = ((-b) + sqrt(discriminant)) / (2 * a);
				r2 = ((-b) - sqrt(discriminant)) / (2 * a);
				// Print two distinct and real roots
				print("\n X = ", r1, terminator: "");
				print("\n X = ", r2, terminator: "");
			}
			else
			{
				// (b²−4ac) < 0
				let imaginary: Double = sqrt(-discriminant) / (2 * a);
				r1 = (-b) / (2 * a);
				r2 = r1;
				// Print two distinct complex roots
				print("\n X = ", r1 ," + ", imaginary ,"i ", terminator: "");
				print("\n X = ", r2 ," - ", imaginary ,"i ", terminator: "");
			}
		}
		print(terminator: "\n");
	}
}
func main()
{
	let task: QuadraticEquation = QuadraticEquation();
	// Case A
	// 4x²+8x+4 = 0
	// a = 4, b = 8, c = 4
	task.squareRoot(4, 8, 4);
	// Case B
	// 7x²+3x+2 = 0
	// a = 7, b = 3, c= 2
	task.squareRoot(7, 3, 2);
	// Case C
	// 5x²+7x+2 = 0
	// a = 5, b = 7, c = 2
	task.squareRoot(5, 7, 2);
}
main();

Output

 Given a :  4.0
 Given b :  8.0
 Given c :  4.0
 X =  -1.0
 X =  -1.0

 Given a :  7.0
 Given b :  3.0
 Given c :  2.0
 X =  -0.214285714285714  +  0.48968961431436 i
 X =  -0.214285714285714  -  0.48968961431436 i

 Given a :  5.0
 Given b :  7.0
 Given c :  2.0
 X =  -0.4
 X =  -1.0
/*
  Kotlin program
  Find square root of quadratic equation
*/
class QuadraticEquation
{
	fun squareRoot(a: Double, b: Double, c: Double): Unit
	{
		// Quadratic formula
		//            _______
		//      −b ± √b2−4ac
		//  x = ————————————
		//          2a
		//
		// Calculate polynomial with an order of 2
		// ax²+bx+c = 0
		var discriminant: Double = (b * b) - (4 * a * c);
		var r1: Double ;
		var r2: Double ;
		// Display parameter
		print("\n Given a : " + a);
		print("\n Given b : " + b);
		print("\n Given c : " + c);
		if (discriminant == 0.0)
		{
			// When (b²−4ac) == 0
			r1 = (-b) / (2 * a);
			r2 = r1;
			// Print two equal and real roots
			print("\n X = " + r1);
			print("\n X = " + r2);
		}
		else
		{
			if (discriminant > 0)
			{
				// When (b²−4ac) > 0
				r1 = ((-b) + Math.sqrt(discriminant)) / (2 * a);
				r2 = ((-b) - Math.sqrt(discriminant)) / (2 * a);
				// Print two distinct and real roots
				print("\n X = " + r1);
				print("\n X = " + r2);
			}
			else
			{
				// (b²−4ac) < 0
				var imaginary: Double = Math.sqrt(-discriminant) / (2 * a);
				r1 = (-b) / (2 * a);
				r2 = r1;
				// Print two distinct complex roots
				print("\n X = " + r1 + " + " + imaginary + "i ");
				print("\n X = " + r2 + " - " + imaginary + "i ");
			}
		}
		print("\n");
	}
}
fun main(args: Array < String > ): Unit
{
	var task: QuadraticEquation = QuadraticEquation();
	// Case A
	// 4x²+8x+4 = 0
	// a = 4, b = 8, c = 4
	task.squareRoot(4.0, 8.0, 4.0);
	// Case B
	// 7x²+3x+2 = 0
	// a = 7, b = 3, c= 2
	task.squareRoot(7.0, 3.0, 2.0);
	// Case C
	// 5x²+7x+2 = 0
	// a = 5, b = 7, c = 2
	task.squareRoot(5.0, 7.0, 2.0);
}

Output

 Given a : 4.0
 Given b : 8.0
 Given c : 4.0
 X = -1.0
 X = -1.0

 Given a : 7.0
 Given b : 3.0
 Given c : 2.0
 X = -0.21428571428571427 + 0.48968961431436026i
 X = -0.21428571428571427 - 0.48968961431436026i

 Given a : 5.0
 Given b : 7.0
 Given c : 2.0
 X = -0.4
 X = -1.0
import math
 
#   Python 3 program
#   Find square root of quadratic equation

class QuadraticEquation :
	def squareRoot(self, a, b, c) :
		#  Quadratic formula
		#             _______
		#       −b ± √b2−4ac
		#   x = ————————————
		#           2a
		# 
		#  Calculate polynomial with an order of 2
		#  ax²+bx+c = 0
		discriminant = (b * b) - (4 * a * c)
		r1 = 0.0
		r2 = 0.0
		#  Display parameter
		print("\n Given a : ", a, end = "")
		print("\n Given b : ", b, end = "")
		print("\n Given c : ", c, end = "")
		if (discriminant == 0) :
			#  When (b²−4ac) == 0
			r1 = int((-b) / (2 * a))
			r2 = r1
			#  Print two equal and real roots
			print("\n X = ", r1, end = "")
			print("\n X = ", r2, end = "")
		else :
			if (discriminant > 0) :
				#  When (b²−4ac) > 0
				r1 = (((-b) + math.sqrt(discriminant)) / (2 * a))
				r2 = (((-b) - math.sqrt(discriminant)) / (2 * a))
				#  Print two distinct and real roots
				print("\n X = ", r1, end = "")
				print("\n X = ", r2, end = "")
			else :
				#  (b²−4ac) < 0 
				imaginary = (math.sqrt(-discriminant) / (2 * a))
				r1 = ((-b) / (2 * a))
				r2 = r1
				#  Print two distinct complex roots 
				print("\n X = ", r1 ," + ", imaginary ,"i ", end = "")
				print("\n X = ", r2 ," - ", imaginary ,"i ", end = "")
			
		
		print(end = "\n")
	

def main() :
	task = QuadraticEquation()
	#  Case A
	#  4x²+8x+4 = 0
	#  a = 4, b = 8, c = 4
	task.squareRoot(4, 8, 4)
	#  Case B
	#  7x²+3x+2 = 0
	#  a = 7, b = 3, c= 2
	task.squareRoot(7, 3, 2)
	#  Case C
	#  5x²+7x+2 = 0
	#  a = 5, b = 7, c = 2
	task.squareRoot(5, 7, 2)

if __name__ == "__main__": main()

Output

 Given a :  4
 Given b :  8
 Given c :  4
 X =  -1
 X =  -1

 Given a :  7
 Given b :  3
 Given c :  2
 X =  -0.21428571428571427  +  0.48968961431436026 i
 X =  -0.21428571428571427  -  0.48968961431436026 i

 Given a :  5
 Given b :  7
 Given c :  2
 X =  -0.4
 X =  -1.0

Resultant Output Explanation

Let's go through the output obtained from the given code:

  1. For the quadratic equation 4x^2 + 8x + 4 = 0, the output shows:

    Given a: 4.000000
Given b: 8.000000
Given c: 4.000000
X = -1.000000
X = -1.000000

    This indicates that the quadratic equation has a single real root (-1) which is repeated twice.

  2. For the quadratic equation 7x^2 + 3x + 2 = 0, the output shows:

    Given a: 7.000000
Given b: 3.000000
Given c: 2.000000
X = -0.214286 + 0.489690i
X = -0.214286 - 0.489690i

    This indicates that the quadratic equation has two distinct complex roots.

  3. For the quadratic equation 5x^2 + 7x + 2 = 0, the output shows:

    Given a: 5.000000
Given b: 7.000000
Given c: 2.000000
X = -0.400000
X = -1.000000

    This indicates that the quadratic equation has two distinct real roots.

Time Complexity

The time complexity of the given code is O(1) because the operations performed are constant for each quadratic equation. Calculating the discriminant, finding square root, and performing arithmetic operations take constant time regardless of the values of 'a', 'b', and 'c'. As a result, the time complexity does not depend on the size of the input.

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