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

##### 1 Answer

See the explanation, please.

#### Explanation:

There is no interval,

There is an interval

It does have a zero, but the zero if in the interval

So, by IVT, there is a

**Note** Irrelevant for this particular problem, but important for understanding the import of IVT:

so there is a

And

so there is a

And so on for every number between

**Note 2**

Because this is not my first rodeo, before answering the question, I looked at the graph of

graph{y = x^3-2x^2-5 [-13.07, 18.99, -9.87, 6.15]}

Clearly this cubic has only one real zero and it is NOT negative.

(Descartes' rule of signs also tells us that there is no positive zeros for this polynomial.)