Question

help please:) JUSTIFICATIONS - POLYNOMIALS! (see below)

Answer 1

\[P(x)=x^3+3x-1\]
Show that the equation P(x)=0 has at least one zero in the interval [-1,1]. You must give a good justification that such a solution exists.

Answer 2

hint : Intermediate Value Theorem

Answer 3

I can just go on my calculator and find the zeros but im not sure if this is a 'good' justification

Answer 4

Hmm - i haven't heard of that one before @ganeshie8

Answer 5

I'm googling it now...

Answer 6

Its easy :

if \(f(a)\) = positive, and \(f(b)\) = negative,
then the function must take a value "\(0\)" in between x = \(a\) and x = \(b\)

Answer 7

THANKS!!!!!!!!!!!!!!!!!!!! I got it :)