Chapter 5: Exercises with Solutions

Section 5.4The Quadratic Formula57. −x 2 + 6 = 7x =⇒ −x 2 − 7x + 6 = 0. The polynomial on the left side does notfactor, so use the quadratic formula:x = −b ± √ b 2 − 4ac2a= 7 ± √ (−7) 2 − 4(−1)(6)2(−1)= 7 ± √ 73−2= − 7 + √ 73, − 7 − √ 732 259. 4x 2 + 3 = −x =⇒ 4x 2 + x + 3 = 0. The polynomial on the left side does notfactor, so use the quadratic formula:x = −b ± √ b 2 − 4ac2a= −1 ± √ 1 2 − 4(4)(3)2(4)= −1 ± √ −478Since √ −47 is not a real number, there are no real solutions.61. To find the x-intercepts, solve the equation f(x) = 0. In other words, solve theequation−4x 2 − 4x − 5 = 0The polynomial on the left side does not factor, so use the quadratic formula:x = −b ± √ b 2 − 4ac2a= 4 ± √ (−4) 2 − 4(−4)(−5)2(−4)= 4 ± √ −64−8Since √ −64 is not a real number, there are no real solutions, and therefore no x-intercepts.Version: Fall 2007