Question

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

Answer 1

See the explanation.

Explanation:

`P(x)` is polynomial function so it's continuous.
`P(2) = 2^3 - 3*2^2+2*2-5 = -5 < 0`
`P(3) = 3^3 - 3*3^2 + 2*3 - 5 = 1 > 0`
Using IVT: `EEx_0 in [2,3] : P(x_0) = 0`