Identify the type of equation : (m+3) (m-2)=0
Answers
Answer:
0=(m+3)(m-2)
=m²-2m+3m-6
=m²+m-6
it is an quadratic equation
Step-by-step explanation:
m
2
+
m
+
1
=
0
is of the form
a
m
2
+
b
m
+
c
=
0
, with
a
=
1
,
b
=
1
,
c
=
1
.
This has discriminant
Δ
given by the formula:
Δ
=
b
2
−
4
a
c
=
1
2
−
(
4
×
1
×
1
)
=
−
3
We can conclude that
m
2
+
m
+
1
=
0
has no real roots.
The roots of
m
2
+
m
+
1
=
0
are given by the quadratic formula:
m
=
−
b
±
√
b
2
−
4
a
c
2
a
=
−
b
±
√
Δ
2
a
Notice that the discriminant is the part inside the square root. So if
Δ
>
0
then the quadratic equation has two distinct real roots. If
Δ
=
0
then it has one repeated real root. If
Δ
<
0
then it has a pair of distinct complex roots.
In our case:
m
=
−
b
±
√
Δ
2
a
=
−
1
±
√
−
3
2
=
−
1
±
i
√
3
2
The number
−
1
+
i
√
3
2
is often denoted by the Greek letter
ω
.
It is the primitive cube root of
1
and is important when finding all roots of a general cubic equation.
Notice that
(
m
−
1
)
(
m
2
+
m
+
1
)
=
m
3
−
1
So
ω
3
=
1