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
.]
For Exercises 8–10,
a. Simplify the expression. Do not rationalize the denominator.
b. Find the values of x for which the expression equals zero.
c. Find the values of x for which the denominator is zero.
4x(4x – 5) – 2x² (4)
8.
-6x(6x + 1) – (–3x²)(6)
(6x + 1)2
9.
(4x – 5)?
-
10. V4 – x² - -() 2)
For Exercises 39–42, multiply the radicals and simplify.
Assume that all variable expressions represent positive real
numbers.
39. (6V5 – 2V3)(2V3 + 5V3)
40. (7V2 – 2VIT)(7V2 + 2V1T)
41. (2c²Va – 5ď Vc)
42. (Vx + 2 + 4)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
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