examday

/TMUA

Consider the polynomial

where $a$ and $b$ are real parameters.

The parameter $a$ varies in the range $0\le a\le1$.

The parameter $b$ varies in the range $-2\le b\le2$.

Assuming that the pair $(a,b)$ is chosen uniformly at random from the rectangle defined by these ranges, find the probability that the equation $f(x)=0$ has three distinct real roots.