( ) 43. = 0 x ( ) The zeros of = 2 −1 + 2x are 4x2 − + 2 = f x x2 −1 − x 3 0 P = 4, a . The of the of and x-intercepts f −1 + 3 = = 2 b c 2 −1, −(−1) − (−1)2 4(4)(2) 1 1 − are and . ± −1 − −1 + 3 3 ± 32 = x = 2 2 2(4) 8 ( ) 47. = 0 G x = ± −31 = 1 not real 8 4 − 9 − 2 = 0 x2 x ( ) The function = 4x2 − + 2 has no P x x −2 = 4, = = a b c real −9, and the graph of has no P x-intercepts. (−9 ) (−9 )2 − ± − ± + 4(4)(−2) 9 81 ( ) = 0 H x 44. 32 4x2 + + 1 = 0 x = = x 2(4) 8 = 9 ± 113 = 4, a 8 = = 1 b c = 4 − 9 − 2 are G x x2 x − 9 113 1, −1 ± 1 − −1 ± 12 − 4(4)(1) = t ( ) = 16 The zeros of 2(4) 8 and . The of the graph of x-intercepts G 9 + 113 8 = −1 ± −15 = not real 8 are and . 9 − 113 9 + 113 ( ) The function = 4x2 + + 1 has no H x x 8 8 real ( ) = 0 x 48. zeros, and the graph of has no H x-intercepts. 5x − 4 − 5 = 0 x2 45. 0 = 4 − 5x + 5 x2 ( ) = 0 F f x 4 − 1 + 2 x2 x = 4, = = 5 = 0 a b c −5, 4 + 2 − 1 x2 x (−5) (−5)2 − ± − 4(4)(5) 5 ± 25 − 80 = 0 = 4, a = = x = 2, = 2(4) 8 b c −1 − 2 ± − 2 4 + 5 ± −55 22 − 4(4)(−1) ± 16
43. P ( x ) = 0 4x2 − x + 2 = 0 The zeros of f ( x ) = 2 x2 −1 + 2x are −1 − 3 a = 4, b = −1, c = 2 and −1 + 3 . The x-intercepts of the of f 2 −(−1) ± (−1)2 − 4(4)(2) 1 ± 1 − 32 are −1 − 3 and −1 + 3 . x = = 2(4) 8 = 1 ± −31 = not real 8 47. 2 2 G ( x ) = 0 4 x2 − 9 x − 2 = 0 The function P ( x ) = 4x2 − x + 2 has no real a = 4, b = −9, c = −2 44. and the graph of P has no x-intercepts. H ( x ) = 0 4x2 + x + 1 = 0 − (−9 ) ± (−9 )2 − 4(4)(−2) 9 ± 81 + 32 x = = 2(4) 8 = 9 ± 113 a = 4, b = 1, c = 1 8 G x = 4 x2 − 9 x − 2 are 9 − 113 −1 ± 12 − 4(4)(1) t = = −1 ± 1 − 16 The zeros of ( ) 2(4) 8 and 9 + 113 . The x-intercepts of the graph of G 8 = −1 ± −15 = not real 8 The function H ( x ) = 4x2 + x + 1 has no real are 9 − 113 8 and 9 + 113 . 8 45. zeros, and the graph of H has no x-intercepts. f ( x ) = 0 48. F ( x ) = 0 5x − 4 x2 − 5 = 0 0 = 4 x2 − 5x + 5 4 x2 − 1 + 2 x = 0 a = 4, b = −5, c = 5 4 x2 + 2 x − 1 = 0 − (−5) ± (−5)2 − 4(4)(5) 5 ± 25 − 80 a = 4, b = 2, c = −1 x = = 2(4) 8 − 2 ± 22 − 4(4)(−1) − 2 ± 4 + 16 5 ± −55
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