Ma 15200 Lesson 14 Section 1.5 Part 1 - Quadratic Equations Worksheet - Purdue University
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6MA 15200
Lesson 14
Section 1.5 (part 1)
, where a, b, and c are real
2
The general form of a quadratic equation is
ax
bx c
0
a . This is a second degree equation.
numbers and
0
There are four ways to possibly solve quadratic equations.
1. Solving by Factoring
2. Solving by the Square Root Property
3. Solving by Completing the Square
4. Solving with the Quadratic Formula
I
Solving by Factoring
Zero-Product Principle: If the product of two algebraic expressions is zero, then at
least one of the factors is equal to zero. If
AB
0, then
A
0 or
B
0.
Steps:
1. If necessary, rewrite the equation in general form (zero on one side, polynomial in
descending order).
2. Factor the polynomial completely.
3. Apply the zero-product principle, setting each factor containing a variable equal
to zero.
4. Solve the resulting equations.
Ex 1: Solve by using factoring.
2
a
)
x
28 3
x
2
b
)
x
121 0
2
c
)
3
x
30
x
0
2
d
)
5
x
12
x
2
1
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