If `alpha, beta` are the roots of `ax^(2) + bx + c = 0 and alpha + h, beta + h` are the roots of `px^(2) + qx + r = 0`, then h =

Options

A. `-1/2(a/b - p/q)`
B. `(b/a - q/p)`
C. `1/2(b/a - q/p)`
D. none of these

Answer

C

Explanation

We have
`alpha + beta = -b/a, alphabeta = c/a`,
`alpha + h + beta + h = -q/p`
`rArr alpha + beta + 2h = -q/p`
`rArr - b/a + 2h = (-q)/(p)`
`rArr h = 1/2 (b/a - q/p)`