Question

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

Answer 1

See the explanation.

Explanation:

`f(x) = 2x^3 + x^2 +2` is continuous function over `R` and hence, over `[-2,-1]`.

`f(-2)=2(-2)^3+(-2)^2+2 = -16+4+2 = -10`
`f(-1)=2(-1)^3+(-1)^2+2 = -2+1+2 = 1`

So, `f(x)` has a root on `[-2,-1]`.