Section 3.4 Zeros of Polynomial Functions

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Presentation transcript:

Section 3.4 Zeros of Polynomial Functions

The Rational Zero Theorem

Example List all possible rational zeros of f(x)=x3-3x2-4x+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?

Example List all possible rational zeros of f(x)=6x3-19x2+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?

Example List all possible rational roots of x4-x3+7x2- 9x-18=0 Starting with the integers, find two roots of the equation using synthetic division.

The Fundamental Theorem of Algebra

The Linear Factorization Theorem

Example Find a fourth-degree polynomial function f(x) with real coefficients that has -1,2 and i as zeros and such that f(1)=- 4

Descartes’s Rule of Signs

Descartes’s Rule of Signs

List all possible rational zeros of the function f(x)=x3+3x2- 6x-8. (d)

Find a third-degree polynomial function f(x) with real coefficients that have 1 and 2i as zeros and such that f(1)=0. (a) (b) (c) (d)

For f(x)=x3- x2+4x- 4 what are all the zeros of the function?

What are the zeros of the function f(x)=x3+2x2+8x+16?

For f(x)=x3- 2x2- 11x+12, what are the zeros of the function?