Program To Find The Roots Of Quadratic equation

Given a quadratic equation in the form ax2 + bx + c, find roots of it. 

quadratic equation
Quadratic Equation

Examples Of Quadratic Equation:

Input  :  a = 1, b = -2, c = 1
Output :  Roots are real and same
          1

Input  :  a = 1, b = 7, c = 12
Output :  Roots are real and different
          -3, -4

Input  :  a = 1, b = 1, c = 1
Output :  Roots are complex 
          -0.5 + i1.73205
          -0.5 - i1.73205

Below is direct formula for finding roots of quadratic equation.

x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a} when ax^2 + bx + c = 0
Quadratic Equation

Here we discuss about following cases:

If b*b < 4*a*c, then roots are complex
(not real).
For example roots of x2 + x + 1, roots are
-0.5 + i1.73205 and -0.5 - i1.73205

If b*b == 4*a*c, then roots are real 
and both roots are same.
For example, roots of x2 - 2x + 1 are 1 and 1

If b*b > 4*a*c, then roots are real 
and different.
For example, roots of x2 - 7x - 12 are 3 and 4

Here implementation of above formula:

Quadratic Equation To Find Roots Through C Program

/* C program to find roots of a quadratic equation */
#include <math.h>
#include <stdio.h>
#include <stdlib.h>

// Prints roots of quadratic equation ax*2 + bx + x
void findRoots(int a, int b, int c)
{
	// If a is 0, then equation is not quadratic, but
	// linear
	if (a == 0) {
		printf("Invalid");
		return;
	}

	int d = b * b - 4 * a * c;
	double sqrt_val = sqrt(abs(d));

	if (d > 0) {
		printf("Roots are real and different \n");
		printf("%f\n%f", (double)(-b + sqrt_val) / (2 * a),
			(double)(-b - sqrt_val) / (2 * a));
	}
	else if (d == 0) {
		printf("Roots are real and same \n");
		printf("%f", -(double)b / (2 * a));
	}
	else // d < 0
	{
		printf("Roots are complex \n");
		printf("%f + i%f\n%f - i%f", -(double)b / (2 * a),
			sqrt_val, -(double)b / (2 * a), sqrt_val);
	}
}

// Driver code
int main()
{
	int a = 1, b = -7, c = 12;

	// Function call
	findRoots(a, b, c);
	return 0;
}

Quadratic Equation To Find Roots Through C++ Program

/* C++ program to find roots of a quadratic equation */
#include <bits/stdc++.h>
using namespace std;

// Prints roots of quadratic equation ax*2 + bx + x
void findRoots(int a, int b, int c)
{
	// If a is 0, then equation is not quadratic, but
	// linear
	if (a == 0) {
		cout << "Invalid";
		return;
	}

	int d = b * b - 4 * a * c;
	double sqrt_val = sqrt(abs(d));

	if (d > 0) {
		cout << "Roots are real and different \n";
		cout << (double)(-b + sqrt_val) / (2 * a) << "\n"
			<< (double)(-b - sqrt_val) / (2 * a);
	}
	else if (d == 0) {
		cout << "Roots are real and same \n";
		cout << -(double)b / (2 * a);
	}
	else // d < 0
	{
		cout << "Roots are complex \n";
		cout << -(double)b / (2 * a) << " + i" << sqrt_val
			<< "\n"
			<< -(double)b / (2 * a) << " - i" << sqrt_val;
	}
}

// Driver code
int main()
{
	int a = 1, b = -7, c = 12;

	// Function call
	findRoots(a, b, c);
	return 0;
}

Quadratic Equation To Find Roots Through Java Program

// Java program to find roots
// of a quadratic equation

import java.io.*;
import static java.lang.Math.*;
class Quadratic {

	// Prints roots of quadratic
	// equation ax * 2 + bx + x
	static void findRoots(int a, int b, int c)
	{
		// If a is 0, then equation is not
		// quadratic, but linear

		if (a == 0) {
			System.out.println("Invalid");
			return;
		}

		int d = b * b - 4 * a * c;
		double sqrt_val = sqrt(abs(d));

		if (d > 0) {
			System.out.println(
				"Roots are real and different \n");

			System.out.println(
				(double)(-b + sqrt_val) / (2 * a) + "\n"
				+ (double)(-b - sqrt_val) / (2 * a));
		}
		else if (d == 0) {
			System.out.println(
				"Roots are real and same \n");

			System.out.println(-(double)b / (2 * a) + "\n"
							+ -(double)b / (2 * a));
		}
		else // d < 0
		{
			System.out.println("Roots are complex \n");

			System.out.println(-(double)b / (2 * a) + " + i"
							+ sqrt_val + "\n"
							+ -(double)b / (2 * a)
							+ " - i" + sqrt_val);
		}
	}

	// Driver code
	public static void main(String args[])
	{

		int a = 1, b = -7, c = 12;
	
		// Function call
		findRoots(a, b, c);
	}
}

// This code is contributed by Sumit Kumar.

Python program to find roots of a Quadratic Equation:

# Python program to find roots
# of a quadratic equation
import math

# Prints roots of quadratic equation
# ax*2 + bx + x


def findRoots(a, b, c):

	# If a is 0, then equation is
	# not quadratic, but linear
	if a == 0:
		print("Invalid")
		return -1
	d = b * b - 4 * a * c
	sqrt_val = math.sqrt(abs(d))

	if d > 0:
		print("Roots are real and different ")
		print((-b + sqrt_val)/(2 * a))
		print((-b - sqrt_val)/(2 * a))
	elif d == 0:
		print("Roots are real and same")
		print(-b / (2*a))
	else: # d<0
		print("Roots are complex")
		print(- b / (2*a), " + i", sqrt_val)
		print(- b / (2*a), " - i", sqrt_val)


# Driver Program
a = 1
b = -7
c = 12

# Function call
findRoots(a, b, c)

# This code is contributed by Sharad Bhardwaj.

C# program to find roots of a quadratic equation:

// C# program to find roots
// of a quadratic equation
using System;

class Quadratic {

	// Prints roots of quadratic
	// equation ax * 2 + bx + x
	void findRoots(int a, int b, int c)
	{

		// If a is 0, then equation is
		// not quadratic, but linear

		if (a == 0) {
			Console.Write("Invalid");
			return;
		}

		int d = b * b - 4 * a * c;
		double sqrt_val = Math.Abs(d);

		if (d > 0) {
			Console.Write(
				"Roots are real and different \n");

			Console.Write(
				(double)(-b + sqrt_val) / (2 * a) + "\n"
				+ (double)(-b - sqrt_val) / (2 * a));
		}

		// d < 0
		else {
			Console.Write("Roots are complex \n");

			Console.Write(-(double)b / (2 * a) + " + i"
						+ sqrt_val + "\n"
						+ -(double)b / (2 * a) + " - i"
						+ sqrt_val);
		}
	}

	// Driver code
	public static void Main()
	{
		Quadratic obj = new Quadratic();
		int a = 1, b = -7, c = 12;
	
		// Function call
		obj.findRoots(a, b, c);
	}
}

// This code is contributed by nitin mittal.

PHP program to find roots of a quadratic equation:

<?php
// PHP program to find roots
// of a quadratic equation

// Prints roots of quadratic
// equation ax*2 + bx + x
function findRoots($a, $b, $c)
{
	// If a is 0, then equation is
	// not quadratic, but linear
	if ($a == 0)
	{
		echo "Invalid";
		return;
	}

	$d = $b * $b - 4 * $a * $c;
	$sqrt_val = sqrt(abs($d));

	if ($d > 0)
	{
		echo "Roots are real and ".
					"different \n";
		echo (-$b + $sqrt_val) / (2 * $a) , "\n",
			(-$b - $sqrt_val) / (2 * $a);
	}
	else if ($d == 0)
	{
		echo "Roots are real and same \n";
		echo -$b / (2 * $a);
	}
	
	// d < 0
	else
	{
		echo "Roots are complex \n";
		echo -$b / (2 * $a) , " + i" ,
			$sqrt_val, "\n" , -$b / (2 * $a),
							" - i", $sqrt_val;
	}
}

// Driver code
$a = 1; $b = -7 ;$c = 12;

// Function call
findRoots($a, $b, $c);

// This code is contributed
// by nitin mittal.
?>

Output:

Roots are real and different 
4.000000
3.000000

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Lingaraj Senapati
Hey There! I am Lingaraj Senapati, the Co-founder of lingarajtechhub.com My skills are Freelance, Web Developer & Designer, Corporate Trainer, Digital Marketer & Youtuber.
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