General continuous random variable problem. given a is uniformly distributed over [-15,11], what is the probability that the roots of the equation are both real?

The roots are both real when the discriminant of the quadratic is positive:



When , say , you have .
When , say , you have .
When , say , you have .

So the quadratic will have two real roots whenever or . The probability of this occurring is



The density function for this random variable is



so