Show that $p(x) = a_nx^n+a...+a_1x+a_0$ either has a root or attains minimum value in R. Show that if $p(x) = a_nx^n +\dots+ a_1x + a_0$ and $a_n > 0$, then either $p(x) = 0$ has a solution, or else $p(x)$ has attains minimum value on $\mathbb{R}$.
I'm sorry I don't know how to even start the problem. I know that if it is an odd degree polynomial then it has roots. 
Thank you. The second part confuses me the most. This is from an undergrad Real Analysis homework. 

Hint: Recall that polynomials are continuous on $\Bbb R$; note that $p(x)\to\infty$ as $x\to\infty$; if $p(x)\lt 0$ for some $x=a$, apply IVT to $p$ on $[a,\infty)$; if $p(x)\gt 0$ for all $x$, recall that $\Bbb R$ has the glb property.
