How, would I go about proving the root exists for:

$\displaystyle x^3+5x^2-4x-1$ in the interval [0,1]

I'm a little lost as to how I should start.

Thanks.

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- Aug 27th 2011, 11:15 AMterrorsquidProving the root of a cubic polynomial
How, would I go about proving the root exists for:

$\displaystyle x^3+5x^2-4x-1$ in the interval [0,1]

I'm a little lost as to how I should start.

Thanks. - Aug 27th 2011, 11:18 AMAckbeetRe: Proving the root of a cubic polynomial
Try using the Intermediate Value Theorem. Does that give you any ideas?

- Aug 27th 2011, 08:04 PMterrorsquidRe: Proving the root of a cubic polynomial
It seems like I'm not doing anything though :D f(0) = -1 and f(1) = 1 and all you say is therefore by the intermediate value there must exist an x such that f(x) = 0 because f(0) is negative and f(1) is positive?

Am I missing any steps in the proof? Just lean on the theorem and do nothing? - Aug 27th 2011, 08:49 PMProve ItRe: Proving the root of a cubic polynomial
- Aug 27th 2011, 09:05 PMCaptainBlackRe: Proving the root of a cubic polynomial
- Aug 28th 2011, 10:12 AMProve ItRe: Proving the root of a cubic polynomial