# Roots of polynomial

• December 10th 2009, 10:18 AM
charikaar
Roots of polynomial
How do i prove that the following has a root between 0 and 4?

$p(x)=x^5-4x^4-10x^2+40x$

Thanks
• December 10th 2009, 10:22 AM
stapel
Use what you learned back in algebra:

What did you see when you graphed this polynomial?

What signs did you get on the values of f(1), f(2), and f(3)?

What did you conclude, on the basis of the Intermediate Value Theorem?

(Wink)
• December 12th 2009, 11:44 AM
SubZero
For F(0)=0
F(1)= 27
F(2)= 8
F(3)= -51
F(4)=0

And we know the graph is continuous since it is a polynomial.

So how would one use the IVT to prove the roots are between F(0) and F(4).
Should it not be between F(2) and F(3)

Thanks