If roots of `ax^(2) + bx + c = 0`are 2 , more than the roots of `px^(2) + qx + r = 0`, then the value of c in terms of p,q and r is

Options

A. `p+q+r`
B. `4p-2q+r`
C. `3p-q+2r`
D. `2p+q-r`

Answer

B

Explanation

Let `f(x) -= px^(2) + qx + r = 0`
Given the quadratic equation whose roots are 2 more than the root of `f(x)` as `ax^(2) +bx + c = 0`
`rArr f(x-2) = ax^(2) + bx + c`
`rArr px^(2) - 4px + 4p + qx - 2q + r = ax^(2) + bx + c`
`rArr px^(2) + (q-4p) x + (4p-2q+r) = ax^(2) + bx + c`
`rArr c= 4p - 2q + r.`