Continuous Function Proof

Hi,

Suppose we have a polynomail of degree n:

p(x) = a0 + a1x + a2x^2 + ... + anx^n

where n is an odd number and "an" (the constant) not equal 0. Show that this polynomail has a real root. You can assume that polynomails are continuous.

So it is pretty intuitive that p(x) as x-> inf is positive and as x-> -inf is negative. I just don't know what facts about polynomials to get

a p(a) = negative number and a p(b) = positive number. Then I know you can use the intermediate value theorem.

Thanks