Question

How do you use the Intermediate Value Theorem to show that the polynomial function `P(x) = x^4 + 2x^3 + 2x^2 - 5x + 3` has a zero in the interval [0, 1]?

Answer 1

You can't. `P(x)` is positive throughout that interval, In fact, that polynomial has no real zeros.

Explanation:

Here is the graph:

`y=x^4+2x^3+2x^2-5x+3`

graph{y=x^4+2x^3+2x^2-5x+3 [-27.77, 37.2, -11.18, 21.25]}