Given the roots of a quadratic equation A and B, the task is to find the equation.
Note: The given roots are integral.
Examples:
Input: A = 2, B = 3
Output: x^2 – (5x) + (6) = 0
x2 – 5x + 6 = 0
x2 -3x -2x + 6 = 0
x(x – 3) – 2(x – 3) = 0
(x – 3) (x – 2) = 0
x = 2, 3Input: A = 5, B = 10
Output: x^2 – (15x) + (50) = 0
Approach: If the roots of a quadratic equation ax2 + bx + c = 0 are A and B then it known that
A + B = – b / a and A * B = c * a.
Now, ax2 + bx + c = 0 can be written as
x2 + (b / a)x + (c / a) = 0 (Since, a != 0)
x2 – (A + B)x + (A * B) = 0, [Since, A + B = -b * a and A * B = c * a]
i.e. x2 – (Sum of the roots)x + Product of the roots = 0
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to find the quadratic// equation whose roots are a and bvoid findEquation(int a, int b){ int sum = (a + b); int product = (a * b); cout << "x^2 - (" << sum << "x) + (" << product << ") = 0";}// Driver codeint main(){ int a = 2, b = 3; findEquation(a, b); return 0;} |
Java
// Java implementation of the above approach class GFG { // Function to find the quadratic // equation whose roots are a and b static void findEquation(int a, int b) { int sum = (a + b); int product = (a * b); System.out.println("x^2 - (" + sum + "x) + (" + product + ") = 0"); } // Driver code public static void main(String args[]) { int a = 2, b = 3; findEquation(a, b); } }// This code is contributed by AnkitRai01 |
Python3
# Python3 implementation of the approach# Function to find the quadratic# equation whose roots are a and bdef findEquation(a, b): summ = (a + b) product = (a * b) print("x^2 - (", summ, "x) + (", product, ") = 0")# Driver codea = 2b = 3findEquation(a, b)# This code is contributed by Mohit Kumar |
C#
// C# implementation of the above approach using System;class GFG { // Function to find the quadratic // equation whose roots are a and b static void findEquation(int a, int b) { int sum = (a + b); int product = (a * b); Console.WriteLine("x^2 - (" + sum + "x) + (" + product + ") = 0"); } // Driver code public static void Main() { int a = 2, b = 3; findEquation(a, b); } }// This code is contributed by CodeMech. |
Javascript
<script>// Javascript implementation of the above approach // Function to find the quadratic // equation whose roots are a and bfunction findEquation(a, b){ var sum = (a + b); var product = (a * b); document.write("x^2 - (" + sum + "x) + (" + product + ") = 0"); }// Driver Code var a = 2, b = 3; findEquation(a, b); // This code is contributed by Ankita saini </script> |
x^2 - (5x) + (6) = 0
Time Complexity: O(1)
Auxiliary Space: O(1)
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
