{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

notes for block day feb 3 or4

# Notes for block day feb 3 or4

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Objectives Section 6.5 Rational Root Theorem! Use the rational, irrational, and imaginary root theorems to locate all the roots of a all the given polynomial equation given Rational Root Theorem This only works if we have integer coefficients. coefficients. Possible rational roots = Find the rational roots of x 3 + x 2 − 3x − 3 = 0 List the possible rational roots: possible Test using substitution or synthetic division division p q Use the rational root Use theorem to find ALL roots theorem 2x3 − x 2 + 2x −1 = 0 Use the rational root Use theorem to find ALL roots theorem x 3 − 2 x 2 − 5 x + 10 = 0 1 The Irrational Root The Theorem Theorem If a + b is a root of a polynomial a− b The Imaginary Root The Theorem Theorem If the imaginary number a + bii iis a root of bs a polynomial equation with real coefficients, then the conjugate a – bi bi also is a root also Imaginary roots also occur in conjugate also occur pairs pairs equation with rational coefficients, then the conjugate is also a root the In other words, irrational roots occur in conjugate pairs. If If 3 is a root, then − 3 is a root If 3, 7 and 2 − i are roots of a polynomial with integer coefficients, find two additional roots. two Find a third-degree polynomial equation degree with rational coefficients that has roots 3 and 1 + i What is the degree of this polynomial? What 2...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online