A quadratic equation with integral coefficients has two different prime numbers as its roots. If the sum of the coefficients of the equation is prime, then the sum of the roots is a. `2` b. `5` c. `7` d. `11`

Options

A. 2
B. 5
C. 7
D. 11

Answer

2

Explanation

Let equation is `a (x - alpha) (x - beta) = 0`, where `alpha, beta` are prime numbers
Sum of coefficients `= a - a(alpha + beta) + aalphabeta`
`= a(alpha - 1) (beta - 1)`, which is prime number
`rArr a = 1` and one of `(alpha - 1) and (beta - 1)` will be 1
Let `alpha - 1 = 1` or `alpha = 2`.
then `beta - 1` will be 2.
So `beta = 3`
Hence, sum of roots = 5