Polynomials and Probability
 

CAUTION: This is more fun (?) math problem than puzzle

given P(x) = ax^2 + bx + c where a,b,c are random (uniformly distributed over the interval [-n,n]) what is the probability that P(x) has real roots?

Are a, b, and c independant?

yes

<bump>

A quadratic polynomial has real roots if its discriminant is non-negative.

Thus the question boils down to: what is the probability that [I]b[SUP]2[/SUP] [/I] >= [I]4ac[/I] ?


I don't think I can go much further without giving too much away.


Paul