Quadratic Equations Worksheet - Rmit University - 2012
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1
2ET1.2: QUADRATIC EQUATIONS
General form
quadratic
A
equation can be rearranged to the form
+
+ =
≠
2
ax
bx c
0
a
0
Examples:
a
b =
c
1.
−
+ =
= 5,
-3,
= 9
2
5
x
3
x
9 0
=
−
⇒
−
+ =
a
b =
c
2.
= 1,
-5,
= 4
2
2
x
5
x
4
x
5
x
4 0
3
=
⇒
=
3.
2
x
2
x
3
2
x
⇒
− =
a
b =
c
= 1,
0,
= -3
2
2
x
3 0
Factorisation
If the equation can be factorised then the ‘null factor law’ can be used to find the solutions:
Null factor law:
If m × n =0,
then m = 0 and/or n = 0
If the product of two or more factors is zero then any one of the individual factors may be
zero and provide a solution for the equation.
Examples:
=
1.
2
y
5
y
2
+
+ =
2
y - 5y = 0
[rearrange to form
ax
bx c
0]
(
)
y y - 5 = 0
[factorise]
y = 0 or y - 5 = 0
[null factor law]
∴ y = 0 or y = 5
y =
2
= 5 × 0:
y =
2
= 5 × 5
0: 0
5: 5
[check by substitution]
ET1.2 – Solving Quadratic Equations
Page 1 of 2
June 2012
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