Given three integers a, b and c such that a + b + c = 0. The task is to find the roots of a quadratic equation ax2 + bx + c = 0.
Examples:
Input: a = 1, b = 2, c = -3
Output: 1, -3
Input: a = -5, b = 3, c = 2
Output: 1, -2.5
Approach: When a + b + c = 0 then the roots of the equation ax2 + bx + c = 0 are always 1 and c / a.
For example,
Take a = 3, b = 2 and c = -5 such that a + b + c = 0
Now, the equation will be 3x2 + 2x – 5 = 0
Solving for x,
3x2 + 5x – 3x – 5 = 0
x * (3x + 5) -1 * (3x + 5) = 0
(x – 1) * (3x + 5) = 0
x = 1, x = (-5 / 3) = (c / a)
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to print the roots of the// quadratic equation when a + b + c = 0void printRoots(long a, long b, long c){ cout << 1 << ", " << c / (a * 1.0);}// Driver codeint main(){ long a = 2; long b = 3; long c = -5; printRoots(a, b, c); return 0;} |
Java
// Java implementation of the approachclass GFG { // Function to print the roots of the // quadratic equation when a + b + c = 0 static void printRoots(long a, long b, long c) { System.out.println(1 + ", " + c / (a * 1.0)); } // Driver Code public static void main (String[] args) { long a = 2; long b = 3; long c = -5; printRoots(a, b, c); }}// This code is contributed by// sanjeev2552 |
Python3
# Python3 implementation of the approach# Function to print the roots of the# quadratic equation when a + b + c = 0def printRoots(a, b, c): print(1, ",", c / (a * 1.0))# Driver codea = 2b = 3c = -5printRoots(a, b, c)# This code is contributed by Mohit Kumar |
C#
// C# implementation of the approachusing System;class GFG{// Function to print the roots of the// quadratic equation when a + b + c = 0static void printRoots(long a, long b, long c){ Console.WriteLine("1, " + c / (a * 1.0));}// Driver codepublic static void Main(){ long a = 2; long b = 3; long c = -5; printRoots(a, b, c);}}// This code is contributed by Nidhi |
PHP
<?php// PHP implementation of the approach// Function to print the roots of the// quadratic equation when a + b + c = 0function printRoots($a, $b, $c){ echo "1"; echo ", "; echo $c / ($a * 1.0);}// Driver code$a = 2;$b = 3;$c = -5;printRoots($a, $b, $c);// This code is contributed by Naman_Garg.?> |
Javascript
<script>// Javascript implementation of the approach// Function to print the roots of the// quadratic equation when a + b + c = 0function printRoots(a, b, c){ document.write(1 + ", " + c / (a * 1.0));}// Driver codevar a = 2;var b = 3;var c = -5;printRoots(a, b, c);// This code is contributed by noob2000.</script> |
Output:
1, -2.5
Time Complexity: O(1), there is only basic arithmetic that happens in constant time.
Auxiliary Space: O(1), no extra space is taken.
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