Rational Root and Complex Conjugates Theorem

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Presentation transcript:

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

Another example

List all possible rational roots. 𝑓 𝑥 =12 𝑥 5 +6 𝑥 4 −7 𝑥 3 +2 𝑥 2 −3𝑥+18

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

Rational Root Theorem

Conjugate Root Theorem If 𝑃(𝑥) is a polynomial with real coefficients, then irrational roots of 𝑃(𝑥) that have the form 𝑎+ 𝑏 occur in conjugate pairs. That is, if 𝑎+ 𝑏 is an irrational root, then 𝑎− 𝑏 is also a root. Likewise for complex roots, if 𝑎+𝑏𝑖 is a root, then 𝑎−𝑏𝑖 is also a root.

Find the lowest degree polynomial with the following roots 3 and 2 – i.

Find the lowest degree polynomial with the following roots

Find the lowest degree polynomial with the following roots