The Rational Root Theorem

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 = 2x3 + 3x - 5

Try y = x3+x2 -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

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