Both roots $x_1$ and $x_2$ of a square equation $x^2+ax+b=0$ can take any value from $-1$ to $1$ with equal probability . Determine the probability densities for coefficients $a$ and $b$.
I think I should use the properties of Vieta's theorem then $x_1+x_2=-a$ and $x_1\cdot x_2=b$.
And I don't know how to solve it further