For Exercises 123–132, write an equation with integer coefficients and the variable x that has the given solution set. [ Hint : Apply the zero product property in reverse. For example, to build an equation whose solution set is { 2 , − 5 2 } we have ( x − 2 ) ( 2 x + 5 ) = 0 , or simply 2 x 2 + x − 10 = 0 .] { 2 , − 2 }
For Exercises 123–132, write an equation with integer coefficients and the variable x that has the given solution set. [ Hint : Apply the zero product property in reverse. For example, to build an equation whose solution set is { 2 , − 5 2 } we have ( x − 2 ) ( 2 x + 5 ) = 0 , or simply 2 x 2 + x − 10 = 0 .] { 2 , − 2 }
Solution Summary: The author explains how the equation with integer coefficients and variable x is x2-2=0.
For Exercises 123–132, write an equation with integer coefficients and the variable x that has the given solution set. [Hint: Apply the zero product property in reverse. For example, to build an equation whose solution set is
{
2
,
−
5
2
}
we have
(
x
−
2
)
(
2
x
+
5
)
=
0
, or simply
2
x
2
+
x
−
10
=
0
.]
Exercises 38–40 will help you prepare for the material covered in
the first section of the next chapter.
In Exercises 38-39, simplify each algebraic expression.
38. (-9x³ + 7x? - 5x + 3) + (13x + 2r? – &x – 6)
39. (7x3 – 8x? + 9x – 6) – (2x – 6x? – 3x + 9)
40. The figures show the graphs of two functions.
y
y
201
10-
....
-20-
flx) = x³
glx) = -0.3x + 4x + 2
For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples.
• In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2).
• Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5).
To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that
x + 4 = (x + 2i)(x – 2i).
115. а. х
- 9
116. а. х?
- 100
117. а. х
- 64
b. x + 9
b. + 100
b. x + 64
118. а. х — 25
119. а. х— 3
120. а. х — 11
b. x + 25
b. x + 3
b. x + 11
In Exercises 20–21, solve each rational equation.
11
20.
x + 4
+ 2
x2 – 16
-
x + 1
21.
x? + 2x – 3
1
1
x + 3
x - 1
||
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