{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stitz-Zeager_College_Algebra_e-book

# The calculator veries this claim x2 x 2 solving x2 9

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: Fundamental Theorem of Algebra 2 + 2i 2 − 2i 225 1 0 0 0 64 ↓ 2 + 2i 8i −16 + 16i −64 1 2 + 2i 8i −16 + 16i 0 ↓ 2 − 2i 8 − 8i 16 − 16i 1 4 8 0 Our quotient polynomial is x2 + 4x + 8. Using the quadratic formula, we obtain the remaining zeros −2 + 2i and −2 − 2i. 3. Using Theorem 3.14, we get f (x) = (x − [2 − 2i])(x − [2 + 2i])(x − [−2 + 2i])(x − [−2 − 2i]). 4. We multiply the linear factors of f (x) which correspond to complex conjugate pairs. We ﬁnd (x − [2 − 2i])(x − [2 + 2i]) = x2 − 4x + 8, and (x − [−2 + 2i])(x − [−2 − 2i]) = x2 + 4x + 8. Our ﬁnal answer f (x) = x2 − 4x + 8 x2 + 4x + 8 . Our last example turns the tables and asks us to manufacture a polynomial with certain properties of its graph and zeros. Example 3.4.4. Find a polynomial p of lowest degree that has integer coeﬃcients and satisﬁes all of the following criteria: • the graph of y = p(x) touches the x-axis at 1 3, 0 • x = 3i is a zero of p. • as x → −∞, p(x) → −∞ • as x → ∞, p(x) → −∞ Solution. To solve this problem, we will need a good understanding of the relationship b...
View Full Document

{[ snackBarMessage ]}