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The Rational Root Theorem

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 = 2x 3 + 3x - 5. Try. y = x 3 +x 2 -17x+15.

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The Rational Root Theorem

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  1. The Rational Root Theorem

  2. 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

  3. Example

  4. Now • Check with division.

  5. Ex • Y = 2x3 + 3x - 5

  6. Try • y = x3+x2 -17x+15

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

  8. 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

  9. 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.

  10. Homework Worksheet 23-39odd

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