Factoring
Zero Product Theorem If the product of two factors is zero then
at least one of the two factors must be zero.
Example
x(x - 1) = 0
implies that either
x = 0
or x = 1
A Review of Factoring
Done by working several examples such as
x^{2} - 3x - 10 = (x - 5)(x + 2)
For a complete review of factoring go to Factoring
and for an interactive tutorial on the AC method for factoring go to http://mathcsjava.emporia.edu/~greenlar/AC/AC.html
The Square Root Method
If the middle term of a quadratic is
zero then the best way to solve is to isolate the x^{2} term and
then take square roots of both sides.
Example
4x^{2} - 9 = 0
Subtract 9 from both sides
to produce
4x^{2} =
9
Divide by 4
x^{2} =
9/4
take the square root
x = +- 3/2
Caution: Don't forget that you get two solutions- the
"plus"
and the "minus" solution.
Quadratic Formula
Recall (otherwise memorize) the quadratic formula: The solutions to
ax^{2 } + bx + c = 0
are
and
We will use this often, so memorize it. Recall that the discriminant
D = b^{2} - 4ac
is a convenient measure of determining how many roots (solutions) there are.
We have:
D |
Number of Roots |
Positive |
2 |
Negative |
0 |
zero |
1 |
Example
The quadratic
3245234543x^{2} - 432523465236432x - 4598674689
has two roots since D is positive.
For more information on the quadratic formula go to The Quadratic Formula