Section 6.5 Theorems about Roots of Polynomial Equations Objective: Students will be able to solve equations using Theorems involving roots. Rational Root.

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Presentation transcript:

Section 6.5 Theorems about Roots of Polynomial Equations Objective: Students will be able to solve equations using Theorems involving roots. Rational Root Theorem Irrational Root Theorem Imaginary Root Theorem Homework

Rational Root Theorem If p/q is in simplest form and is a rational root of the polynomial equation …., with integer coefficients, then p must be a factor of …, and q must be a factor of ….

Irrational Root Theorem Let a and b be rational numbers and let a+√b is a root of a polynomial equation with rational coefficients, then the conjugate a-√b is also a root.

Imaginary Root Theorem If the imaginary number a+bi is a root of a polynomial equation with real coefficients, then the conjugate a-bi is also a root.

6.5 Homework Page 333: 1-6 even, 12-24 even