# Intermediate value theorem

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Define Intermediate-Value theorem

Using this theorem, show that there is a root of P(x)=x^3+x^2+x-1 in the closed interval [0,1].

https://brainmass.com/math/calculus-and-analysis/intermediate-value-theorem-16641

#### Solution Preview

P(x) is continuous. Since P(0)=-1 and P(1)=2 there must be a number in such that (Since 0 is between -1 and 2). We can do even better. We have

Therefore there is a root between ...

#### Solution Summary

This defines Intermediate-Value theorem and uses it in a proof.

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