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  4. The quadratic equation 2x2-(a3+8a-1)x+a2-4a=0 possesses roots of opposite sign. Then

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Q. The quadratic equation $2x^{2}-\left(a^{3}+8a-1\right)x+a^{2}-4a=0$ possesses roots of opposite sign. Then

WBJEEWBJEE 2012Complex Numbers and Quadratic Equations

Solution:

Since, roots are opposite sign.
$\therefore $ Product of the roots $ < 0$
$\Rightarrow a^{2}-4 a < 0$
$\Rightarrow a(a-4) < 0$
$\Rightarrow 0 < a < 4$