College Algebra 9th txtbk

86 CHAPTER 1 EQUATIONS AND INEQUALITIES
ZZZ CAUTION ZZZ
1. One side of an equation must be 0 before the zero product property can be
applied. So
does not mean that x 1 4 or x 5 4. See Example 1, part C, for
the correct solution of this equation.
2. The equations
x 2 6x 5 4
(x 1)(x 5) 4
2x 2 3x
and
2x 3
are not equivalent. The first has solution set 50, 3 26, but the second has solution
set 5 3 26. The root x 0 is lost when each member of the first equation is divided
by the variable x. See Example 1, part D, for the correct solution of this equation.
Never divide both sides of an equation by an expression containing the variable
for which you are solving. You may be dividing by 0, which of course is
not allowed.
Z Using the Square Root Property to Solve
Quadratic Equations
We now turn our attention to quadratic equations that do not have the first-degree term—
that is, equations of the special form
ax 2 c 0 a 0
The method of solution of this special form makes direct use of the square root property:
Z SQUARE ROOT PROPERTY
If A 2 C, then A 1C.
The use of the square root property is illustrated in Example 2.
EXAMPLE 2 Using the Square Root Property
Solve using the square root property:
(A) 9x 2 7 0 (B) 3x 2 27 0 (C) (x 1 2) 2 5 4
SOLUTIONS (A) 9x 2 7 0
Add 7 to both sides.
9x 2 7
Divide both sides by 9.
x 2 7 9
x 7
B 9 17 3
Apply the square root property; don’t forget the !
Solution set: e 17
3 , 17
3 f