In the quadratic equation `4x^(2) - 2 ( a + c - 1) x + ac - b = 0`
`(a gt b gt c)`

Options

A. both roots are greater then a
B. both roots are less then c
C. both roots lie between `c//2 and a//2`
D. exactly one of the roots lies between `c//2 and a//2` .

Answer

4

Explanation

Here, ` f(x) = (2x - a) (2x - c) + (2x - b)`. So
`f((a)/(2)) = a - b, f ((c)/(2)) = c - b`
Now, `f((a)/(2)) f ((c)/(2)) = (a - b) (c -b) lt 0 (a gt b gt c)`
Hence, exactly one of the roots lies between c/2 and a/2.