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

Answer

B

Explanation

We have, `alpha + beta = - (b)/(a), alpha beta = (c)/(a) and, alpha + h + beta + h = -(q)/(p), (alpha + h) (beta+h) = (r)/(p)`
`rArr" "alpha + beta + 2h = - (q)/(p) rArr - (b)/(a) + 2h = - (q)/(p)" "[because alpha + beta = - (b)/(a)]`
`rArr" "h = (1)/(2) ((b)/(a)-(q)/(p))`