Given the roots of a quadratic equation A and B, the task is to find the equation.
Note: The given roots are integral.
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, 3
Input: 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:
x^2 - (5x) + (6) = 0
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