Transcript Equations - BakerMath.org

Solving Quadratic Equations by
Factoring
1
2
3
Terminology
Zero Factor Theorem
Methods for Solving
Terms
2
Terminology
Quadratic Equation in x
Definition
An equation that can be
written in the form
ax2 + bx + c =0,
where a≠0
Example
x2  5x  4 x
x2  5x  4x  0
a  1, b  5, c  4
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Zero Factor Theorem
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
If p and q are algebraic expressions, then pq=0 if
and only if p=0 or q=0
 Example:

(x+2)(2X-4)=0; x+2=0 and/or 2x-4=0
Steps
 Get
all variables & constants set equal to zero
 Factor
 Set each factor equal to zero
 Solve each factor individually
 CHECK YOUR ANSWER
Zeros of the Function: Graphs
4
Zeros of the
Function
y
Zeros of the
Function
x
Solving by Factoring
5

Solve 3x2=10-x
More Solving by Factoring
6

Solve the equation x2 + 16 =8x
When to Use What
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
Multiples of a variable or constant
 Example: 12x 3  8 x 2  0
 GCF

3 terms without a multiple of a variable or constant
 Example:
x 2  5 x  3
 Rainbow
Method