) = 0 = 0 51. 55. 6 − − 2 = x2 x 16 − 8x + 1 = 0 x2 0 (4 P − 1)2 = 0 x (3x (2x g − 2) + 1) = 0 ( 4 − 1 = 0 ⇒ = 1 ( x x 3x − 2 = 0 or 2 + 1 = 0 x 4 x 2 1 ) x =− ( ) = − + The only real zero of 16 8x 1 is g x x2 . 1 4 = x x 3 2 The only of the graph of is . x-intercept g 1 4 = 6 − − 2 are and . x2 x − 2 ( The zeros of P x 3 1 ) 2 ) of the graph of are P − 1 = 0 2 52. and . 2 − + = 4 12 9 0 x2 x 3 ( ) = 0 H x (2 − 3)2 = 0 56. x F 6 + − 2 = 0 x2 x ( 2x − 3 = 0 ⇒ = 3 (3x (2 x + − = 2) 1) 0 x The 2 x ( ) + = − = = − + 3x 2 0 or 2 1 0 The only real zero of 4x2 12 9 is x F x x . 3 2 1 2 − = = x x The only of the graph of is . x-intercept F 3 3 2 2 1 2 ( ) The zeros of = 6 2 H x + − 2 are and . x − x 3 2 ) 53. = 0 The of the of are and . x-intercepts H − 2 1 − −15 = 10x2 19 x 3 2 G 0 ( ( ) 57. = 0 (5x (2x G x + 3) − 5) x = 0 + = − 5x 3 0 or 2 5 x + x2 − = 2 1 = x 0 3 =− x ⎛ 1 ⎞ = 5 x 5 2 (0) (2) ( ) 2 ⎜ + 2 ⎟ = x2 x The zeros of = 10 − 19 −15 are G x x2 x − 3 ⎝ ⎠ and − 2 2 5 x + − = 2 2x 1 0 . The of the graph of are 5 x-intercepts G − 3 = 2, = 2 2 , = −1 a b c ( ) 2 and . 5 = x 5 2 −(2 ± 2 )
51. g ( x ) = 0 16 x2 − 8x + 1 = 0 (4 x − 1)2 = 0 4 x − 1 = 0 ⇒ x = 1 4 55. P ( x ) = 0 6 x2 − x − 2 = 0 (3x − 2) (2x + 1) = 0 3x − 2 = 0 or 2 x + 1 = 0 2 1 =− The only real zero of g ( x ) = 16 x2 − 8x + 1 is 1 . 4 x = x 3 2 The only x-intercept of the graph of g is 1 . 4 The zeros of P ( x ) = 6 x2 − x − 2 are − 1 2 and 2 . 3 52. F ( x ) = 0 4 x2 − 12 x + 9 = 0 (2 x − 3)2 = 0 2x − 3 = 0 ⇒ x = 3 2 The only real zero of F ( x ) = 4x2 − 12 x + 9 is 3 . 56. The of the graph of P are − 1 2 H ( x ) = 0 6 x2 + x − 2 = 0 (3x + 2) (2 x − 1) = 0 3x + 2 = 0 or 2 x − 1 = 0 2 1 and 2 . 3 2 The only x-intercept of the graph of F is 3 . x = − x = 3 2 2 2 1 2 The zeros of H ( x ) = 6 x + x − 2 are − and . 3 2 53. G ( x ) = 0 10x2 − 19 x −15 = 0 (5x + 3) (2x − 5) = 0 57. The x-intercepts of the of H are − 2 3 G ( x ) = 0 and 1 . 2 5x + 3 = 0 or 2 x − 5 = 0 x2 + 2 x − 1 = 3 x =− x = 5 ⎛ 1 ⎞ 5 2 The zeros of G ( x ) = 10 x2 − 19 x −15 are − 3 and 2 ⎜ x2 + ⎝ 2 2 x − ⎟ = (0) (2) ⎠ 5 2 x + 2 2x − 1 = 0 5 . The x-intercepts of the graph of G are − 3 a = 2, b = 2 2 , c = −1 2 and 5 . 5 ( ) x = −(2 2 ) ± 2
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