 The Rational Root Theorem.  Is a useful way to find your initial guess when you are trying to find the zeroes (roots) of the polynomial.  THIS IS JUST.

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The Rational Root Theorem

 Is a useful way to find your initial guess when you are trying to find the zeroes (roots) of the polynomial.  THIS IS JUST A TEST NOT ANSWER

Example

Now  Check with division.

Ex  Y = 2x 3 + 3x - 5

Try  y = x 3 +x 2 -17x+15

The fundamental Theorem of Algebra  Each nth degree polynomial can be factored in n linear terms

The fundamental Theorem of Algebra  Counting imaginary roots and multiple roots, an nth degree polynomial equation has exactly n roots, the related polynomial function has exactly n zeros

The fundamental Theorem of Algebra  If a and b are rational numbers and  b is an irrational number and if a +  b is a root of a polynomial equation with rational coefficients, then the conjugate a -  b is also a root. This is also true for imaginary numbers. A + bi also has a root A – bi.

Homework Worksheet 23-39odd

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