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Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: 34x − 10 √ 5 x = 17 (mult. 1), x = ± 2 (each mult. 1) (j) p(x) = 25x5 − 105x4 + 174x3 − 142x2 + 57x − 9 x = 3 (mult. 2), x = 1 (mult. 3) 5 (k) p(x) = x5 − 60x3 − 80x2 + 960x + 2304 x = −4 (mult. 3), x = 6 (mult. 2) (l) p(x) = x3 − 7x2 + x − 7 x = 7 (mult. 1) (m) p(x) = 90x4 − 399x3 + 622x2 − 399x + 90 2 x = 3 (mult. 1), x = 3 (mult. 1), x = 5 (mult. 1), x = 2 3 3 5 (mult. 1) (n) p(x) = 9x3 − 5x2 − x √ x = 0 (mult. 1), x = 5±18 61 (each has mult. 1) 2. We choose q (x) = 72x3 − 6x2 − 7x + 1 = 72 · f (x). Clearly f (x) = 0 if and only if q (x) = 0 1 so they have the same real zeros. In this case, x = − 3 , x = 1 and x = 1 are the real zeros 6 4 of both f and q . 3. (a) (b) (c) (d) 1 (−∞, 2 ) ∪ (4, 5) {−2} ∪ [1, 3] (−∞, −1] ∪ [3, ∞) √ √ (−∞, 1 − 2) ∪ (1 + 2, 5) 1 ∪ [1, ∞) 2 √√ (f) (−∞, −2) ∪ − 2, 2 (g) [−2, 2] (h) (−∞, −1) ∪ (−1, 0) ∪ (2, ∞) (e) − 3.4 Complex Zeros and the Fundamental Theorem of Algebra 3.4 219 Complex Zeros and the Fundamental...
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