Stitz-Zeager_College_Algebra_e-book

We formalize the concepts of vertical and horizontal

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

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

Unformatted text preview: can find the remaining zeros using the Quadratic Formula, if necessary. Using the techniques developed in Section 3.3, we get 3.4 Complex Zeros and the Fundamental Theorem of Algebra 1 2 1 2 −1 3 223 12 −20 19 −6 −2 1 ↓ 6 −7 6 0 −1 12 −14 12 0 −2 0 ↓ 6 −4 4 2 12 −8 8 40 ↓ −4 4 −4 12 −12 12 0 √ i Our quotient is 12x2 − 12x + 12, whose zeros we find to be 1±2 3 . From Theorem 3.14, we know f has exactly 5 zeros, counting multiplicities, and as such we have the zero 1 with 2 1 multiplicity 2, and the zeros − 3 , √ 1+i 3 2 and √ 1−i 3 2, each of multiplicity 1. 2. Applying Theorem 3.14, we are guaranteed that f factors as 1 f (x) = 12 x − 2 2 1 x+ 3 √ 1+i 3 x− 2 √ 1−i 3 x− 2 A true test of Theorem 3.14 (and a student’s mettle!) would be to take the factored form of f (x) in the previous example and multiply it out8 to see that it really does reduce to the formula f (x) = 12x5 − 20x4 + 19x3 − 6x2 − 2x + 1. When factoring a polynomial using Theorem 3.14,...
View Full Document

Ask a homework question - tutors are online