How to find the values of a and b? If the polynomial 6x4 + 8x3 - 5x2 + ax + b is exactly divisible by the polynomial 2x2 - 5, then find the values of a and b.

The roots of $2x^2-5$ must be roots of our polynomial:
$$\left\lbrace
\begin{array}{c}
6\cdot\frac{25}4+15\sqrt{\frac52}-\frac{25}2+\sqrt{\frac52}a+b=0\\
\phantom{1}\\
6\cdot\frac{25}4-15\sqrt{\frac52}-\frac{25}2-\sqrt{\frac52}a+b=0
\end{array}
\right.$$
Adding up the equations you get
$$50+2b=0$$
And substracting them:
$$30\sqrt{\frac52}+2\sqrt{\frac52}a=0$$
So $a=-15$, $b=-25$.
