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

Question

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?

Just notice that $f(0)=0$ and $f'(0)=-2015<0$. – Asydot Sep 26 '15 at 13:59 — Asydot, Sep 26 '15 at 13:59

score 0 · Answer 1 · answered Sep 26 '15 at 13:58

0

At $x=o$ the polynomial has a root which is your third real root.

See this if you need further hint

answered Sep 26 '15 at 13:58

Kushal Bhuyan

7,110

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

1 Answers1