How do I use the intermediate value theorem to determine whether a polynomial function has a solution over a given interval?

1 Answer
Bernardo Russo G. Ferreira
May 16, 2015

To answer this question, we need to know what the intermediate value theorem says.

The theorem basically sates that:
For a given continuous function f(x) in a given interval [a,b], for some y between f(a) and f(b), there is a value c in the interval to which f(c) = y.

It's application to determining whether there is a solution in an interval is to test it's upper and lower bound.

Let's say that our f(x) is such that f(x) = x^2 - 6*x + 8 and we want to know if there is a solution between 1 and 3 (in the [1,3] interval).
f(1) = 3
f(3) = -1
From the theorem (since all polynomials are continuous), we know that there is a c in [1,3] such that f(c) = 0 (-1 <= 0 <= 3)//

Hope it helps.

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