The real values of 'a' for which the quadratic equation `2x^2 - (a^3 + 8a - 1) x + a^2 - 4a = 0` possess roots of opposite sign is given by:

Options

A. `a gt 5`
B. `0 lt a lt 4`
C. `a gt 0`
D. `a gt 7`

Answer

B

Explanation

The roots of the given equation will be of opposite signs if they are real and their product is negative.
i.e. Discriminant `ge` 0 and Product of roots `lt 0`
`rArr" "(a^(3) + 8a - 1)^(2)-8(a^(2) - 4a) ge 0 and (a^(2)-4a)/(2) lt 0`
`rArr" "a^(2) - 4a lt 0 [because a^(2)-4a lt 0 rArr (a^(3) + 8a - 1)^(2) -8(a^(2) - 4a) ge 0]`
`rarr" "0 lt a lt 4`