# How to prove that the equation $x^5-1102x^4-2015x=0$ has at least three real roots? [duplicate]

I've already used the Intermediate Value Theorem to show that there is at least one real root.
$$f(1)=-3116<0$$
$$f(-1)=912>0$$
Using IVT to $$N=0,$$ there exists $$c \in (-1,1)\;$$ such that $$\;f(c)=0.$$
I can use Rolle's Theorem to show that there is at least $$2$$ real roots, but how do I show that the equation has at least three real roots?

## marked as duplicate by LutzL, Community♦Sep 26 '15 at 14:02

• Just notice that $f(0)=0$ and $f'(0)=-2015<0$. – Asydot Sep 26 '15 at 13:59
At $x=o$ the polynomial has a root which is your third real root.