8-5 Rational Zero Theorem

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Presentation transcript:

8-5 Rational Zero Theorem Objective: To identify all possible rational zeros of a polynomial function by using the rational zero theorem. To find zeros of polynomial functions.

Rational Zero Theorem

Corollary (Integral Zero Theorem)

Possible Rational Roots Example q p Factors of p: Factors of q: Possible zeros: (12 possible zeros)

Example 1 List all the possible rational zeros of these functions. p(x) = 3x3 – 5x2 – 11x + 3

Example 2 List all the possible rational zeros of these functions and state whether they are positive or negative. f(x) = 3x3 + 9x2 + x – 10 + - i

Example 3 Find all the rational zeros for this function. f(x) = x4 + 10x3 + 33x2 + 38x + 8 + - i

Example 4 Find all the zeros for this function. f(x) = x3 – 4x2 – 2x + 20 + - i

Assignment 8-5 pg 513 #18-24 even 32, 34