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Rational Root and Complex Conjugates Theorem

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Rational Root and Complex Conjugates Theorem

Rational Root Theorem

• Used to find possible rational roots (solutions) to a polynomial

• Possible Roots : P/Q

• Where P represents the factors of the constant of the polynomial and Q represents the factors of the leading coefficient

Rational Root Theorem

9,9,

3,3,

1,1

2,1:

9,3,1:

912112)( 23

iespossibilitso

xxxxf

Rational Root Theorem

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912112)( 23 xxxxf

Page 5: Rational Root and Complex Conjugates Theorem. Rational Root Theorem Used to find possible rational roots (solutions) to a polynomial Possible Roots :

Rational Root Theorem122)(. 45 xxxxfSolve

Rational Root Theorem

factors theof alllist then and roots List the

464)(. 23 xxxxfSolve

Complex Conjugates Theorem

• If a + bi is a zero of the polynomial, then a – bi is a zero also.

• Ex. Find the polynomial whose zeros include 3 and 2 – i

Page 8: Rational Root and Complex Conjugates Theorem. Rational Root Theorem Used to find possible rational roots (solutions) to a polynomial Possible Roots :

Find the lowest degree polynomial with the following roots

i 6,5,3

Page 9: Rational Root and Complex Conjugates Theorem. Rational Root Theorem Used to find possible rational roots (solutions) to a polynomial Possible Roots :

Find the lowest degree polynomial with the following roots

oftymultipliciawith

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