# How do you use the Intermediate Value Theorem to show that the polynomial function #x^3 - 2x^2 + 3x = 5# has a zero in the interval [1, 2]?

##### 2 Answers

Here's one way to do it.

#### Explanation:

Let

(Needed because the intermediate value theorem is a theorem about *functions* .)

Observe that the equation

So the question now is to show that for at least one number

by the intermediate value theorem, there is at least one number

That is, the original equation has a solution.

Assuming you meant

Evaluate

#### Explanation:

Note:

**equation**; it is **not** a polynomial **function**. Reference to an equation having a zero in an interval is meaningless.

That only leaves

Since