Suppose $b$ a random number in the interval $(-3,3)$ Which the probability of the equation $x^2+bx+1=0$ have a least a real root? 
Suppose $b$ a random number in the interval $(-3,3)$ Which the probability of the equation $x^2+bx+1=0$ have a least a real root?

I don't know how to start this exercise. Can someone help me?

Hint: The polynomial $f(x) = x^2+bx+1$ has a real root if there is an $x$ s.t. $f(x) \le 0$ is satisfied [make sure you can see why].
The minimum of $f(x)$ is achieved when $df(x)/dx = 2x+b$ is 0, at $x=\frac{-b}{2}$.
The values of $b \in (-3,3)$ s.t. the inequality $f(-\frac{b}{2}) = \frac{b^2}{4} - \frac{b^2}{2}+1 =-\frac{b^2}{4}+1 \le 0$ is satisfied
are $|b| \ge 2$.
Note that $|b| \ge 2$ holds for precisely $\frac{1}{3}$ of $b \in (-3,3)$, so the probability is $\frac{1}{3}$.
