FSC Algebra Equations Zero Factor Questions

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SECTION 1.2 Quadratic Equations
101
me length of a side of the
ngth x Width x Height
timeters, and its square ba
9(x – 18)
1.2 Assess Your Understanding
“Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.
1. Factor: x? – 5x – 6 (pp. 49-55)
4. True or False Vx2 = |x]. (pp. 23-24)
2. Factor: 2x – x – 3 (pp. 49-55)
5. Complete the square of x2 + 5x. Factor the new
3. The solution set of the equation (1-3) (3x + 5) = 0
expression. (p. 56)
is
.(p. 13)
Concepts and Vocabulary
6. The quantity b² – 4ac is called the
of a
quadratic equation. If it is
, the equation has no real
solution.
7. True or False Quadratic equations always have two real
solutions.
8. True or False If the discriminant of a quadratic equation
is positive, then the equation has two solutions that are
negatives of one another.
9. A quadratic equation is sometimes called a equation.
(a) first-degree (b) second-degree
(c) third-degree (d) fourth-degree
10. Which of the following quadratic equations is in standard
form?
(a) x2 – 7x = 5
(b) 9 = x2
(c) (x + 5)(x – 4) = 0 (d) 0 = 5×2 – 6x – 1
144
Divide each side by 9.
se the Square Root Method.
Skill Building
In Problems 11–30, solve each equation by factoring.
11. r? – 9x = 0
12. x2 + 4x = 0
13. x2 – 25 = 0
14. x2 – 9 = 0
15. z2 + 2 – 6 = 0
16. y2 + 7y + 6 = 0
17. 2×2 – 5x – 3 = 0
18. 3×2 + 5x + 2 = 0
Onclude that the sheet me:
19. 312 – 48 = 0
20. 2y2 – 50 = 0
21. x(x – 8) + 12 = 0
22. x(x + 4) = 12
23. 4×2 + 9 = 12x
24. 25×2 + 16 = 40x
25. 6(p2 – 1) = 5p
26. 2 (2u? – 4u) + 3 = 0
6
12
27. 6r – 5
–
28. x +
=
7
4(x – 2)
29.
x – 3
=
3 -3
+
x x(x – 3
x(x – 3)
5
30.
x + 4
= 4 +
3
x-2
X
x
luced the method of factoring:
40-1603) introduced a methor
In Problems 31–36, solve each equation by the Square Root Method.
31. x2 = 25
32. x2 = 36
2.
33. (x – 1)2 = 4
glect the negative roots (if ther.
are roots of negative quantities
500s.
34. (x + 2)2 = 1
35. (2y + 3)2 = 9
36. (32 – 2)2 = 4
In Problems 37–42, solve each equation by completing the square.
3
37. r2 + 4x = 21
38. x2 – 6x = 13
39. x2
za
0
2
16
of known area. Complete the
1
1
40. x2 + x
3 3
= 0
41. 3×2 + x
0
42. 2×2 – 3x – 1 = 0
2
35 = 0 by letting x = U +1
+ z) – 85 = 0
12z – 85) = 0
In Problems 43–66, find the real solutions, if any, of each equation. Use the quadratic formula.
43. x2 – 4x + 2 = 0
44. x2 + 4x + 2 = 0
45. x2 – 4x – 1 = 0
finish the solution.
46. x² + 6x + 1 = 0
47. 2×2 – 5x + 3 = 0
48. 2×2 + 5x + 3 = 0
rmula Look at equation 4
49. 4y2 – y + 2 = 0
50. 412 + + + 1 = 0
51. 4×2 = 1 – 2x
2
and then
V6² – 4ac
2a
S
52. 2r? = 1 – 2x
53. 4×2 = 9x
54. 5x = 4×2
is now 0 and the left side isa
mis difference of two squares
-atic formula, and moreover
55. 9t2 – 61 + 1 = 0
3
56. 4u2 – 6u + 9 = 0
57.
12
–
1 1
4 2
0
ch is sometimes useful
.
4
it hundrate Equation
page to
. 1. 25,73, 37,47
52