`(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

Options

A. one roots is less than 0, the is posititve, the other is negative.
B. exactly one of the roots lies in (0,1)
C. both the roots lie in (0,1)
D. at least one of the roots lies in (0,1)

Answer

1

Explanation

`af(1) lt 0 and f(0) f(1) gt 0`
`rArr af(1) lt 0 and af(0) lt 0`
Hence, both the numbers 0 and 1 lie between the roots.