Probability with random-coefficient quadratic equation

Let A, B, and C be independent random variables, and consider the random-coefficient quadratic equation $\displaystyle Ax^2 + Bx + C = 0 $

What is the probability that the equation has real roots $\displaystyle x$ when A, B, and C take on the value 1 with probability $\displaystyle p \in [0,1], $ and -1 with probability $\displaystyle 1 - p $?

What is the probability that the equation has real roots $\displaystyle x$ when A, B, and C a have a $\displaystyle \cup(0,1)$ distribution?

Embarrassed to ask but...

Quote:

Originally Posted by

**awkward** .

where the region of integration in all the triple integrals is the region where $\displaystyle 0 \leq A \leq 1$, $\displaystyle 0 \leq B \leq 1$, $\displaystyle 0 \leq C \leq 1$, and $\displaystyle B^2 - 4AC \geq 0$.

I am confused with the $\displaystyle B^2 - 4AC \geq 0$ part that you wrote.

I must be doing the wrong thing. If there A, B, and C are all the same, and given the pdf of a uniform distribution is

$\displaystyle f(x) = \frac{1}{b-a} $ for $\displaystyle a< x <b $ where 1 = 0 and a = 0, won't I just get a probability of one when integrating?? Where do I apply $\displaystyle B^2 - 4AC \geq 0$?