# Find bounds on the real zeros of the polynomial function

Posted By Admin @ November 26, 2022

How to Find Bounds on the Real Zeros of a Polynomial Function

Using synthetic division, we will investigate a couple of methods that can be used to find bounds on the real zeros of a polynomial function. One method uses a synthetic division to find the nth degree polynomial function. Using the nth degree polynomial to find the corresponding quadratic equation gives us a useful approximation of the real zeros. Similarly, the quadratic quotient function can be used to find the remainders.

The nth degree polynomial is x3 - 2x2 + x. Using the Linear Factorization Theorem, we find f(x) is x3 - 2x3 + x - 4. If we use the Polynomial Function Bounds Theorem, we can find f(x) is x3 + x2 - 3 x3 + x2 - 7.

The Polynomial Function Binds Theorem gives us a complete graph of the polynomial function, which we can use to find the real zeros. The theorem also gives us the upper and lower bounds, which we can use to make the bounds sharper. The theorem omits the most important bit of information, however.

The Polynomial Function Binds is not a perfect solution to the problem. However, it is a good start. The Intermediate Value Theorem can be used to approximate the real zeros of the polynomial function.

Another method to find bounds on the real zeros is to check out the Rational Zeros Theorem. It consists of a few short steps that give you an indication of the possibilities of finding positive and negative real zeros.

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