- Find the discriminant and the solution of each equation in parts (a)-(c). If
necessary, round to the nearest hundredth.
a. x2 — 6x + 5 = 0 b. x2 + x — 20 = 0 c. 2x2 — 7x — 3 = 0
d. Reasoning When the discriminant is a perfect square, are the solutions rational
or irrational? Explain.
Challenge 46. Reasoning The solutions of any quadratic equation ax2 + bx + c = 0 are
-b + \Zb2 - 4 ac , —b — V i?2 - 4ac
25 and 25---------’
a. Find a formula for the sum of the solutions.
b. One solution of 2x2 + 3x — 104 = 0 is -8. Use the formula you found in part (a)
to find the second solution.
(^R eason ing For each condition given, tell whether o x 2 + bx + c = Owill
always, sometimes, or never have two solutions.- b2 < 4ac 48. b2 = 0 49. ac < 0
St a n d a r d i ze d Test Pr ep
^SAT/ACTShort
, R e s p o n s e- What are the approximate solutions of the equation x2 — 7x + 3 = 0?
CD -6.54, 0.46 CD -6.54, -0.46 CD -0.46, 6.54 CD 0.46, 6.54
51. Which of the following relations is a function?
C D {(1,2), (3, 5), (1,4), (2,3)}
C D {(-5 , 6), (0, 9), (—1, 2), (0, 6)}C D {(8, 2), (6, 3), (6,11), (-8 , 2)}
CD {(-1 , 3), (7, 3), (-7 , 2), (4, 5)}- What equation do you get when you solve 3a - b = 2c for bl
CD b = —3a + 2c C D b = 3a — 2c CD b = 3a + 2c CD b = —3 a - 2c - What are the approximate solutions of the equation - v2 — |x + 1 = 0? Use a
graphing calculator.
CD 1-07, 2.77 CD 1-16, 2.59 CD 0.87,10.38 - Suppose the line through points (n, 6) and (1,2) is parallel to the graph of
2x + y = 3. Find the value of n. Show your work.
CD 0.19,16.01
Mixed Review
ASolve each equation by completing the square.- s2 — 10s + 13 = 0 56. m2 + 3m = —2
Get Read y! To p r e p a r e f o r Lesso n 9 - 7 , d o Ex e r c i se s 5 8 - 6 1.
Graph each function.- y = 2 x 59. y = 3x 60. 3 / = ( 3 ) ^
See Lesson 9-5.- 3w2 + 18m —1 = 0
^ See Lesson 7-6.588 Ch ap t e r 9 Quadratic Functions and Equat ions