Question

For the intermediate value theorem why do you think it is necessary for the signs of f(a) and f(b) to be different in order to guarantee there is a zero between a and b. If it is the case that the signs of f(a) and f(b) are the same, does that mean the function f(x) cannot have a zero between a and b? Explain. The following link may be helpful: https://www.mathsisfun.com/algebra/intermediate-value-theorem.html