If the roots of the quadratic equation `ax^(2)+bx-b=0`, where `a`, `b in R` such that `a*b gt 0`, are `alpha` and `beta`, then the value of `log_(|(beta-1)|)|(alpha-1)|` is

Options

A. (a) `1`
B. (b) `-1`
C. (c) `0`
D. (d) none of these

Answer

B

Explanation

`(b)` Roots of `ax^(2)+bx-b=0` are `alpha` and `beta`
`:.alpha+beta=(-b)/(a)` and `alphabeta=(-b)/(a)`
`:.alpha+beta-alpha*beta=0`
`:. (alpha-1)(beta-1)=1`
`:. |alpha-1|*|beta-1|=1`
`:.log_(|(beta-1)|)|(alpha-1)|=-1`