Question

The real values of 'a' for which the quadratic equation $2x^2-(a^3+8a-1)x+a^2-4a=0$ possesses roots of opposite signs are given by :

• A. a > 6
• B. a > 9
• C. 0 < a < 4
• D. a < 0

Answer 1

The correct option is C 0 < a < 4

The roots of the given equation will be of opposite signs if they are real and their product is negative, i.e.,
$D\ge 0$ and product of roots < 0
$\Rightarrow (a^3+8a-1{)}^2-8(a^2-4a)\ge 0$
and $a^2-4a<0$
$[\because a^2-4a<0\Rightarrow (a^3+8a-1{)}^2-8]$
$\Rightarrow 0<a<4.$