# How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^4 -10x^2 + 3# has one zero?

##### 1 Answer

Explanation below :)

#### Explanation:

The intermediate value theorem states that if **continuous** function, and there exist two points

For example, if

This theorem is often used to find zeroes of functions: if the function you're working with is continue, and you can find two points

So, in your case, we need to find two points with image, respectively, negative and positive. Unfortunately, there is no algorithm to do so, you have to train your instinct a little bit. In this case for example,

We're done, since

I'll post the graph of the function only for checking purpose.

graph{x^4-10x^2+3 [-2.738, 2.737, -1.366, 1.372]}