Chapter 5: Exercises with Solutions

Section 5.4The Quadratic Formulax = −b ± √ b 2 − 4ac2a= 1 ± √ (−1) 2 − 4(1)(−7)2(1)= 1 ± √ 292= 1 + √ 29, 1 − √ 292 245. Use factoring and the principle of zero products:4x 2 + 4x − 1 = −2=⇒ 4x 2 + 4x + 1 = 0=⇒ (2x + 1) 2 = 0=⇒ x = − 1 2Alternatively, use the quadratic formula x = −b ± √ b 2 − 4ac.2a47. The polynomial 2x 2 + 4x + 6 does not factor, so use the quadratic formula:x = −b ± √ b 2 − 4ac2a= −4 ± √ 4 2 − 4(2)(6)2(2)= −4 ± √ −324Since √ −32 is not a real number, there are no real solutions.49. −3x 2 + 2x − 13 = −5 =⇒ −3x 2 + 2x − 8 = 0. The polynomial on the left sidedoes not factor, so use the quadratic formula:x = −b ± √ b 2 − 4ac2a= −2 ± √ 2 2 − 4(−3)(−8)2(−3)= −2 ± √ −92−6Since √ −92 is not a real number, there are no real solutions.Version: Fall 2007