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.
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.
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:
Time Complexity: O(1)
- Program to find the Roots of Quadratic equation
- Program to find number of solutions in Quadratic Equation
- Absolute difference between sum and product of roots of a quartic equation
- Roots of Unity
- Sum of first N terms of Quadratic Sequence 3 + 7 + 13 + ...
- Minimize the sum of roots of a given polynomial
- Maximum and Minimum value of a quadratic function
- Seeds (Or Seed Roots) of a number
- Bakhshali Approximation for computing square roots
- Find the number of primitive roots modulo prime
- Program for Stirling Interpolation Formula
- Legendre's formula (Given p and n, find the largest x such that p^x divides n!)
- Print first n Fibonacci Numbers using direct formula
- Newton's Divided Difference Interpolation Formula
- Program to implement Inverse Interpolation using Lagrange Formula
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.