1. It is a second-degree equation (the highest variable exponent is 2).
3. We want to take advantage of the zero property of multiplication in the fact that if a⋅b=0 then it must follow that each factor separately offers a solution to the product being zero: a=0or b=0.
5. One, when no linear term is present (no x term), such as x2=16. Two, when the equation is already in the form (ax+b)2=d.
7. x=6, x=3
9. x=2−5, x=3−1
11. x=5, x=−5
13. x=2−3, x=23
15. x=−2
17. x=0, x=7−3
19. x=−6, x=6
21. x=6, x=−4
23. x=1, x=−2
25. x=−2, x=11
27. x=3±22
29. z=32, z=−21
31. x=43±17
33. Not real
35. One rational
37. Two real; rational
39. x=2−1±17
41. x=65±13
43. x=8−1±17
45. x≈0.131 and x≈2.535
47. x≈−6.7 and x≈1.7
49. ax2+bx+cx2+abxx2+abx+4a2b2(x+2ab)2x+2abx=0=a−c=a−c+4a2b=4a2b2−4ac=±4a2b2−4ac=2a−b±b2−4ac
51. x(x+10)=119; 7 ft. and 17 ft.
53. maximum at x=70
55. The quadratic equation would be (100x−0.5x2)−(60x+300)=300. The two values of x are 20 and 60.
57. 3 feet
Licenses & Attributions
CC licensed content, Specific attribution
College Algebra.Provided by: OpenStaxAuthored by: OpenStax College Algebra.Located at: https://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface.License: CC BY: Attribution.