How do i prove that the following has a root between 0 and 4?

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

Thanks

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- Dec 10th 2009, 10:18 AMcharikaarRoots of polynomial
How do i prove that the following has a root between 0 and 4?

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

Thanks - Dec 10th 2009, 10:22 AMstapel
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) - Dec 12th 2009, 11:44 AMSubZero
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