probability of a quadratic function has real roots

Question

Let $A, B$ be independent random variables with uniform distribution on $[0,1]$.

What is the probability that the quadratic equation $x^2 + 2A x + B = 0$ has real roots?

I obtained the answer $\frac{1}{3}$, is it correct?

Answer 1

Yes, your answer is correct.

The probability of $$ x^2 + 2A x + B = 0$$ having real roots is the probability of $$ P(B\le A^2) $$

Which is $$ \int _0 ^1 x^2 dx = 1/3 $$