Here's a question from Real Analysis textbook:
Let $p(x)=a_0 + a_1 x + \ldots + a_n x^n$. If $a_0 a_n <0$, show that $p$ has at least two real roots.
I'm not sure how to even prove this and I think this is wrong since the polynomial $p(x)=x^3-x^2+x-1$ satisfies the above conditions but then has only one root.
Am I wrong somewhere?