Answer:
0
"
a
×
b
c
d
e
=
,
.
∴
or
o
r
x
2
+
5
6
←
−
(
)
1
If
→
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Answers & Comments
Answer:
By factorizing first and then applying the multiplication property of zero, we can solve a quadratic equation.
Explanation:
One of the properties of
0
is that :
"Anything multiplied by
0
is equal to
0
"
So, if we have an equation where:
a
×
b
×
c
×
d
×
e
=
0
,
then because of the multiplication property of
0
, we will know that at least one of the factors being multiplied must be equal to
0
.
Since we can't know which one is the
0
, we consider each in turn being
0
.
∴
a
=
0
or
b
=
0
or
c
=
0
or
d
=
0
o
r
e
=
0
However, this is only true for FACTORS.
So to apply this concept in solving a quadratic (or cubic, quartic, etc.) equation, start by factorizing to find the factors.
Then let each factor be equal to
0
and solve to find the possible values of the variable.
x
2
+
5
x
=
6
←
of no help in this form:
x
2
+
5
x
−
6
=
0
←
make it equal to
0
(
x
+
6
)
(
x
−
1
)
=
0
←
two factors multiply to give
0
Let each be equal to
0
If
x
+
6
=
0
→
x
=
−
6
If
x
−
1
=
0
→
x
=
1
By factorizing first and then applying the multiplication property of zero, we can solve the quadratic equation.