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Quadratic Equation Notes O Level IGCSE Math Notes.

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Curriculum ReadyQuadratic Equations
Quadratic Equations
1
100% Quadratc Equatons
Mathletics 100% © 3P Learning
Quadratic Equations
SERIES TOPIC
K 7
If
x
2
=
16
, is
x
=
4
the only answer?Is it possible to nd soluons for
x
in
ax
2
+
bx
+
c
=
0
based only on
a
,
b
and
c
?How many soluons does a quadrac equaon have?
QUADRATIC EQUATIONS
A quadrac equaon is an equaon where the highest index is
2
(squared). These are a lile more complicated to solve than linear equaons, and may have no real soluons at all.
What do I know now that I didn't know before?
Answer these quesons,
before
working through the chapter.
I used to think:
Answer these quesons,
afer
working through the chapter.
But now I think:
If
x
2
=
16
, is
x
=
4
the only answer?Is it possible to nd soluons for
x
in
ax
2
+
bx
+
c
=
0
based only on
a
,
b
and
c
?How many soluons does a quadrac equaon have?
2
100% Quadratc Equatons
Mathletics 100% © 3P Learning
Quadratic Equations
SERIES TOPIC
K 7
Basics
Quadratic Equations
If the highest index of the variable is
2 (
eg.
x
2
or
y
2
)
then the equaon is not linear, but is called a
quadrac equaon
.
To nd the variable by itself on one side, the square root is used to change
x
2
to
x
. But the
square root must be used on both sides.
Solve for
x
in the quadrac equaon
x x x x x x
2 16 342 16 16 34 1622218933
22222 2
!!
+ =+ - = -====
^ h
Each quadrac equaon can have one, two or no real soluons. The above example has two soluons
(
x
= -3
or
x
= 3
). Somemes the soluons will have to be le in surd form like this next example:
Solve for
x
x x x x x
4 20 04 20555
2222 2
!!
- =====
^ h
This equaon has the two possible soluons
x
5=
or
x
5=
Here is an example of a quadrac equaon with no real soluons:
Solve for
x
in the quadrac equaon
x x x x x
3 8 43 8 8 4 83331244
2222
!
+ =-+ - =- -= -=-= -
This does not have any real soluons since no real number is the square root of a negave number.
Subtract
16
from both sidesDivide both sides by
2
Because
3 9
2
=
and
3 9
2
- =
^ h
Find the square root of both sides

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