`(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 `|b| gt |a + c|`, then

Options

A. one roots of f(x)=0 is positive, the other is negative
B. exactly one of the roots of f(x) = 0 lie in (-1,1)
C. 1 lies between the roots of f(x) = 0
D. both the roots of f(x) = 0 are less than 1

Answer

2

Explanation

`b^(2) gt (a + c)^(2)`
`rArr (a+c-b) (a + c+b) lt 0`
`rArr f(-1) f(1) lt 0`
So, there is exactly one root in `(-1,1)`.