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  4. The real values of ' a ' for which the quadratic equation 2 x2-(a3+8 a-1) x+a2-4 a=0 possess roots of opposite sign is given by:

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

Complex Numbers and Quadratic Equations

Solution:

$2 x^2-\left(a^3+8 a-1\right) x+\left(a^2-4 a\right)=0$
Since the roots are of opposite sign.
$ f(0)< 0$
$ \Rightarrow a^2-4 a< 0$
$ \Rightarrow a(a-4)< 0 $
$\Rightarrow a \in(0,4)$