Rational Root and Complex Conjugates Theorem

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Presentation transcript:

Rational Root and Complex Conjugates Theorem

Fundamental Theorem of Algebra Every polynomial of degree n has exactly n roots.

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

Find all possible rational roots and then find ones that work.

Another example

Rational Root Theorem

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

Find the lowest degree polynomial with the following roots

Find the lowest degree polynomial with the following roots