If `alpha` , `beta` are the roots of `ax^(2) + bx+ c = 0" and a+h, ``beta`+h are the roots of `px^(2) + qx+ r = 0` then what is h equal to ?

Options

A. `1/2 (b/a-q/p)`
B. `1/2 (-b/a+q/p)`
C. ` 1/2 (b/p+q/a)`
D. `1/2 (-b/p+q/a)`

Answer

A

Explanation

`:' alpha + beta = - b/a and alpha beta = c/a`
Also, `alpha + h + beta + h = - q/p`
`rArr alpha + beta + 2 h = - q/p`
`rArr 2h = -q/p + b/a`
`( :' alpha + beta = - b/a)`
`h= 1/2 [b/a-q/p]`