Game Development Reference
In-Depth Information
Quadratic Equations
A quadratic equation is a polynomial of the second degree. In other words, one of
its terms possesses an exponent of 2. A quadratic equation usually consists of
three terms. Here is the standard form of a quadratic equation:
ax
2
þ bx þ c ¼
0
In such an equation, the constant
a
cannot be equal to 0, because then the variable
x
is also 0. As already mentioned, the degree of the quadratic equation is based on
the value of the exponent for the variable
x
, which is 2. On the other hand, the
constants
c
and
b
can be zero.
To solve quadratic equations, you can employ a set of techniques. Using this set
of techniques provides a much easier way to solve quadratic equations than if you
approach them intuitively. To understand how to use these techniques, consider
working with the following equation:
x
2
¼
36
Such an equation falls into the standard quadratic category, but to see it as such,
you must realize that
b
and
c
are equal to zero. Think of the equation as
x
2
þ
0
x
36
¼
0
Since little is accomplished by using the second term, you can drop it. You are
then left with this equation:
x
2
36
¼
0
To solve for the value of
x
, you can draw from the discussion in Chapter 8 and
factor the equation. To factor the equation, you draw on observations con-
cerning the difference of two squares. You take the square roots of both of the
terms in the expression. Accordingly, while
x x ¼ x
2
,
it also stands that
p
36
p
36
If you then rearrange the resulting term so that you show the
difference of two squares, your work appears as follows:
¼
36
:
x
2
36
¼
0
Set equal to 0
:
p
36
p
36
ðx
Þðx þ
Þ¼
0
Factor
:
p
p
36
36
x
¼
0or
x þ
¼
0
Solve for each factor
:
p
36
x ¼
p
x ¼
:
or
36
Possible solution set
