Section 5.5 Theorems about Roots of Polynomial Equations.

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Presentation transcript:

Section 5.5 Theorems about Roots of Polynomial Equations

Rational Root Theorem All possible rational roots are in the list of: factors of the constant factors of the L.C. Example:Any rational root for will be in the list:

Find all the roots of:

What are the rational roots of:

Conjugate Root Theorem A polynomial with rational coefficients will always have complex roots that are complex conjugate pairs. This is also true of irrational roots but only if the coefficients are rational. For example, if 2 - 3i is a root then 2 + 3i is also a root. If √5 is a root then -√5 is also a root.

Ifare roots, what are two other roots?

What is a third-degree polynomial function with rational coefficients that has roots -4 and 2i?