Question

`(af(mu) lt 0)` is the necessary and sufficient condition for a particular real number `mu` to lie between the roots of a quadratic equations `f(x) =0,` where `f(x) = ax^(2) + bx + c`. Again if `f(mu_(1)) f(mu_(2)) lt 0`, then exactly one of the roots will lie between `mu_(1)` and `mu_(2)`.
If `a(a+b+c) lt 0 lt (a+b+c)c`, then
A. one roots is less than 0, the other is greater than 1
B. one roots lies in `(-oo,0)` and other in `(0,1)`
C. both the roots lie in `(0,1)`
D. one roots lies in (0,1) and other in `(1,oo)`

Answer 1

Correct Answer - 2
`f(0) f(1) lt 0 and af(1) gt 0`
`rArr f(0) f(1) lt 0 and af(0) lt 0`
Hence, exctly one root lie in (0,1) and 0 lie between the roots.