3.4_bzca5e

3.4_bzca5e - Section 3.4 Zeros of Polynomial Functions The...

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Section 3.4 Zeros of Polynomial Functions

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The Rational Zero Theorem

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Example List all possible rational zeros of f(x)=x 3 -3x 2 -4x+12 Find one of the zeros of the function using synthetic division, then factor the remaining polynomial. What are all of the zeros of the function? How can the graph below help you find the zeros?
Example List all possible rational zeros of f(x)=6x 3 -19x 2 +2x+3 Starting with the integers, find one zero of the function using synthetic division, then factor the remaining polynomial. What are all of the zeros of the function?

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Example List all possible rational roots of x 4 -x 3 +7x 2 - 9x-18=0 Starting with the integers, find two roots of the equation using synthetic division. The graph below will help you easily find those roots. Factor the remaining polynomial. What are all of the roots of the equation? The graph below will NOT help you find the imaginary roots. Why?

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4 3 Notice that the roots for our most recent problem (x -x 7 9 18 0; degree 4) were 3i,2,-1 x x + - - = ±
The Fundamental Theorem of Algebra

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Remember that having roots of 3, -2, etc. are complex roots because 3 can be written 3+0i and -2 can be written as -2+0i.
Theorem

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3.4_bzca5e - Section 3.4 Zeros of Polynomial Functions The...

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