4.5 solve quadratic equations by finding square roots
TRANSCRIPT
4.5 Solve Quadratic Equations by Finding Square Roots
EXAMPLE 1 Use properties of square roots
Simplify the expression.
5= 4a.
80 516=
= 3 14b.
6 21 126= 9 14=
c.
481 =
4
81=
2 9
d.
716 =
7
16=
47
GUIDED PRACTICEGUIDED PRACTICE for Example 1
271.
3 3
982.
2 7ANSWER
ANSWER
GUIDED PRACTICEGUIDED PRACTICE for Example 1
3.
6 5
10 15
4. 8 28
14 4ANSWER
ANSWER
GUIDED PRACTICEGUIDED PRACTICE for Example 1
5.
3 8
964
6. 154
215ANSWER
ANSWER
GUIDED PRACTICEGUIDED PRACTICE for Example 1
7. 1125
8. 3649
511
76 ANSWER
ANSWER
EXAMPLE 2 Rationalize denominators of fractions.
Simplify (a) 52
and 3
7 + 2
SOLUTION
(a) 52
210=
=5
2
=5
2
2
2
(b)
EXAMPLE 2 Rationalize denominators of fractions.
SOLUTION
(b) 3
7 + 2=
3
7 + 2 7 – 2
7 – 2
= 21 – 3 2
49 – 7 + 7 – 2 2 2
= 21 – 3 247
EXAMPLE 3 Solve a quadratic equation
Solve 3x2 + 5 = 41.
3x2 + 5 = 41 Write original equation.
3x2 = 36 Subtract 5 from each side.
x2 = 12 Divide each side by 3.
x =
+ 12 Take square roots of each side.
x =
+ 4 3
x =
+ 2 3
Product property
Simplify.
EXAMPLE 3 Solve a quadratic equation
ANSWER
The solutions are and 2 3 2 3–
Check the solutions by substituting them into the original equation.
3x2 + 5 = 413( )2 + 5 = 412 3
?
41 = 413(12) + 5 = 41
?
3x2 + 5 = 413( )2 + 5 = 41 – 2 3
?
41 = 413(12) + 5 = 41
?
EXAMPLE 4 Standardized Test Practice
SOLUTION
15
(z + 3)2 = 7 Write original equation.
(z + 3)2 = 35 Multiply each side by 5.
z + 3 = + 35 Take square roots of each side.
z = –3 + 35 Subtract 3 from each side.
The solutions are –3 + and –3 – 35 35
EXAMPLE 4 Standardized Test Practice
ANSWER
The correct answer is C.
GUIDED PRACTICE for Examples 2, 3, and 4GUIDED PRACTICE
Simplify the expression.
9.
530
65
10. 98
24
3
11. 1712
516
ANSWER
ANSWER
ANSWER
12.
39921
1921
– 21 – 3 522
13. – 6
7 – 5
8 – 2 115
14. 2
4 + 11
ANSWER
ANSWER
ANSWER
– 9 + 774
for Examples 2, 3, and 4GUIDED PRACTICE
15. – 1
9 + 7
32 + 4 361
16. 4
8 – 3
ANSWER
ANSWER
for Examples 2, 3, and 4GUIDED PRACTICE
17.
Solve the equation.
5x2 = 80
+ 4
18. z2 – 7 = 29
+ 6
19. 3(x – 2)2 = 40
120
32 +
ANSWER
ANSWER
ANSWER