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  4. The discriminant of 2 x2-k x-9=0 is 108 . Find the number of values exist for k.

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Q. The discriminant of $2 x^2-k x-9=0$ is 108 . Find the number of values exist for $k$.

Quadratic Equations

Solution:

Given: $2 x^2-k x-9=0$
Discriminant $(\Delta)=b^2-4 a c$
$\Rightarrow(-k)^2+4(2)(9)=108$
$\Rightarrow k^2+72=108$
$\Rightarrow k^2=36, k= \pm 6$