In a quadratic equation `ax^(2)- bx + c = 0, a,b,c` are distinct primes and the product of the sum of the roots and product of the root is `91/9`. Find the difference between the sum of the roots and the product of the roots.

Options

A. 2
B. 3
C. 4
D. Cannot be determined

Answer

A

Explanation

Product of the sum of the roots and product of the roots is `91/9`, i.e.,
`(b/axxc/a) = 91/9`
`(bc)/(a^(2)) = 91/9`
`(bc)/(axxa) = (13xx7)/(3xx3)`
`rArr b/a=13/3,c/a=7/3` or `b/a=7/3, c/a = 13/3`
The required difference is `13/3 - 7/3 = 2`.