XAT 2025 Linear and Quadratic Equations — Previous Year Question

Consider the quadratic function $f(x) = ax^2 + bx + a$ having two irrational roots, with $a$ and $b$ being two positive integers, such that $a, b \le 9$.

If all such permissible pairs $(a, b)$ are equally likely, what is the probability that $a + b$ is greater than 9?