358 CHAPTER 3 Polynomial and Rational Functions Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* 95. ƒ1x2 = x4 + 2x3 - 3x2 + 24x - 180 96. ƒ1x2 = x3 - x2 - 8x + 12 97. ƒ1x2 = x4 + x3 - 9x2 + 11x - 4 98. ƒ1x2 = x3 - 14x + 8 99. ƒ1x2 = 2x5 + 11x4 + 16x3 + 15x2 + 36x 100. ƒ1x2 = 3x3 - 9x2 - 31x + 5 101. ƒ1x2 = x5 - 6x4 + 14x3 - 20x2 + 24x - 16 102. ƒ1x2 = 9x4 + 30x3 + 241x2 + 720x + 600 103. ƒ1x2 = 2x4 - x3 + 7x2 - 4x - 4 104. ƒ1x2 = 32x4 - 188x3 + 261x2 + 54x - 27 105. ƒ1x2 = 5x3 - 9x2 + 28x + 6 106. ƒ1x2 = 4x3 + 3x2 + 8x + 6 107. ƒ1x2 = x4 + 29x2 + 100 108. ƒ1x2 = x4 + 4x3 + 6x2 + 4x + 1 109. ƒ1x2 = x4 + 2x2 + 1 110. ƒ1x2 = x4 - 8x3 + 24x2 - 32x + 16 111. ƒ1x2 = x4 - 6x3 + 7x2 112. ƒ1x2 = 4x4 - 65x2 + 16 113. ƒ1x2 = x4 - 8x3 + 29x2 - 66x + 72 114. ƒ1x2 = 12x4 - 43x3 + 50x2 + 38x - 12 115. ƒ1x2 = x6 - 9x4 - 16x2 + 144 116. ƒ1x2 = x6 - x5 - 26x4 + 44x3 + 91x2 - 139x + 30 *The authors would like to thank Aileen Solomon of Trident Technical College for preparing and suggesting the inclusion of Exercises 95–108. If c and d are complex numbers, prove each statement. (Hint: Let c = a + bi and d = m+ ni and form all the conjugates, the sums, and the products.) 117. c + d = c + d 118. c # d = c # d 119. a = a for any real number a 120. c2 = 1c22 In 1545, a method of solving a cubic equation of the form x3 + mx = n, developed by Niccolo Tartaglia, was published in the Ars Magna, a work by Girolamo Cardano. The formula for finding the one real solution of the equation is x = C3 n 2 + Ba n 2b 2 + a m 3 b 3 - C3 -n 2 + Ba n 2b 2 + a m 3 b 3 . (Data from Gullberg, J., Mathematics from the Birth of Numbers, W.W. Norton & Company.) Use the formula to solve each equation for the one real solution. 121. x3 + 9x = 26 122. x3 + 15x = 124
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