Stitz-Zeager_College_Algebra_e-book

2 tells 6 us y 2 3 is the horizontal asymptote the

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Unformatted text preview: r classmates, build a polynomial p with integer coefficients such that x = −2 − i is a zero of p, p has a local maximum at the point (4, 0) and p(x) → −∞ as x→∞ 228 3.4.2 Polynomial Functions Answers 1. (a) i5 = i4 · i = 1 · i = i (b) i304 = (i4 )76 = 176 = 1 2. (a) z + w = 5 + 3i (b) w − z = −1 − 5i (c) z · w = 10 + 5i 3. (a) √ −49 = 7i √√ (b) −9 −16 = (3i) · (4i) = 12i2 = −12 4. (a) x = 2 ± 3i (c) (2i)3 = 8i3 = −8i (d) (−i)23 = −i23 = −i20 · i3 = (−1)(−i) = i z 2 11 =+i w 5 5 w 2 11 (e) = −i z 25 25 (f) w3 = 2 − 11i (d) √ (−9)(−16) = 144 = 12 √√ (d) 49 −4 = 7 · 2i = 14i (c) √ 1 29 (b) x = − ± i 3 3 5. (a) x2 − 2x + 5 = (x − (1 + 2i))(x − (1 − 2i)) Zeros: x = 1 ± 2i (b) x3 − 2x2 + 9x − 18 = (x − 2) x2 + 9 = (x − 2)(x − 3i)(x + 3i) Zeros: x = 2, ±3i √ √ 1 3 3 3 +6x2 +6x+5 = (x+5)(x2 +x+1) = (x+5) x − − 1 + i x− − − i (c) x 2 2 2 2 √ 1 3 Zeros: x = −5, x = − ± i 2 2 (d) 3x3 − 13x2 + 43x − 13 = (3x − 1)...
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