Let $a, b \in R, a \neq 0$ be such that the equation, $a x^2- 2 \mathrm{bx}+5=0$ has a repeated root $\alpha$, which is also a root of the equation, $x^2-2 b x-10=0$. If $\beta$ is the other root of this equation, then $\alpha^2+\beta^2$ is equal to:
