L16 - Lecture 16, Part I: Section 2.5 Zeros of Polynomial...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 16, Part I: Section 2.5 Zeros of Polynomial Functions Linear Factorization Theorem Every polynomial function u1D453 ( u1D465 ) of degree u1D45B > 0 can be factored into u1D45B linear factors (not necessarily distinct) of the form u1D453 ( u1D465 ) = u1D44E u1D45B ( u1D465 − u1D450 1 )( u1D465 − u1D450 2 ) ⋅ ⋅ ⋅ ( u1D465 − u1D450 u1D45B ) where u1D450 1 , u1D450 2 , . . . , u1D450 u1D45B are complex numbers. That is, every polynomial function of degree u1D45B > has exactly n (not necessarily distinct) zeros in the complex number system. ex. Find all zeros of u1D453 ( u1D465 ) = u1D465 4 − 16 in the complex number system. The Rational Zero Test If the polynomial u1D453 ( u1D465 ) = u1D44E u1D45B u1D465 u1D45B + u1D44E u1D45B − 1 u1D465 u1D45B − 1 + ⋅ ⋅ ⋅ + u1D44E 1 u1D465 + u1D44E has integer coefficients, then every rational zero of u1D453 has the form u1D45D u1D45E (in lowest terms), where u1D45D is a factor of u1D44E and u1D45E is a factor of u1D44E u1D45B...
View Full Document

This note was uploaded on 12/27/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

Page1 / 10

L16 - Lecture 16, Part I: Section 2.5 Zeros of Polynomial...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online