Chapter 14
QUADRATIC EQUATIONS AND INEQUALITIES
The techniques used to solve linear equations presented in Chapter 4
are significantly different than those used to solve quadratic equations.
Whereas the primary means by which linear equations are solved still ap-
ply (that is, it is still permissible to add or subtract the same quantity from
both sides of an equation), quadratic equations require you to factor, com-
plete the square, or apply the quadratic formula in order to isolate x and
solve the equation. This chapter also discusses techniques used to solve and
graph quadratic inequalities.
Chapter 4 explains how to solve linear equations—equations like
x + 4 = 12, where the highest power of the variable is 1. Chapter 7
explains how to solve and graph linear inequalities, things like x + 4 > 12.
This chapter ups the ante and explains how to solve quadratic equations
and inequalities, which contain a variable raised to the second power.
Quadratic equations have UP TO two different real number solutions,
and something called the discriminant helps you gure out exactly how
many there are without calculating them. You can use one of three
methods to solve a quadratic equation: factoring, completing the square,
and the quadratic formula. Factoring is probably the easiest, but it
works only when you can actually factor the polynomial. The quadratic
formula and completing the square always work but they are a little
more complicated.
Finally, this chapter explains how to solve inequalities containing x
2
. You
need to use something called “critical numbers,” and they’re explained as
well. You’ll need them again in Chapter 21 to solve rational inequalities.
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