Write the set of value of k for which the quadratic

The given quadric equation is $2 x^{2}+k x-8=0$, and roots are real.

Then find the value of k.

Here, $a=2, b=k$ and, $c=-8$

As we know that $D=b^{2}-4 a c$

Putting the value of $a=2, b=k$ and,$c=-8$

$=(k)^{2}-4 \times 2 \times(-8)$

$=k^{2}+64$

The given equation will have real roots, if $D>0$

I.e., $k^{2}+64>0$ which is true for all real values of $k$

Therefore, for all real values of k, the given equation has real roots.