Hi So I have to prove the following:

If with and and n is an even positive integer, then prove that p has at least two distinct roots.

So my proof looks a little like this so far:

p is continuous on .

and .

Hence such that:

.

...

At this point Im stuck. I found, via graphing example polynomials, that the negative values cause the polynomial to have two distinct roots, but how to state this mathematically to finish the proof?

Any suggestions would be appreciated thanks.