Let $p(x) = a_0 + a_1x + a_2x^2 + \cdots + a_nx^n$ with $a_0,a_1,\dots,a_n \in \Bbb R$. Prove that if $a_0a_n < 0$, then $p$ has a positive root.
Show that a polynomial has at least one positive solution/root.