Question

How do you use the Intermediate Value Theorem to show that the polynomial function `f(x) = x^2 − x + 1` has a root in the interval [-1, 6]?

Answer 1

The function can be written as

`f(x)=x^2-x+1=(x-1/2)^2+3/4>0` so it does not have any roots in `[-1,6]` because if she did we should have `f(x)=0` which is a contradiction.