Question

Suppose you are trying to find the zeros for a polynomial p(x). After making a table of values you have discovered that p(2)= - 4 and p(3) = 5. You make a sketch of the graph of p(x). What do you see on your graph that makes you realize that there must be a zero between 2 and 3? Explain how your observation leads you to a logical conclusion that there must be a zero in that interval. Suppose you have used the Rational Zeros Theorem to test every possible rational zero and have not found one between 2 and 3. How is that possible?

Answer 1

Can you see the change in sign there in that interval which illustrates a fact that a root is present somewhere between [2,3]