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Byju's Answer
Standard XII
Mathematics
Roots of a Quadratic Equation
Find the root...
Question
Find the roots of given equation:
z
3
−
3
z
2
+
6
z
−
4
=
0
A
1
,
1
+
√
3
i
,
1
−
√
3
i
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B
1
,
1
+
√
2
i
,
1
−
√
2
i
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C
3
,
1
+
√
3
i
,
1
−
√
3
i
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D
All of them
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Solution
The correct option is
A
1
,
1
+
√
3
i
,
1
−
√
3
i
In this case, for
p
(
z
)
=
z
3
−
3
z
2
+
6
z
−
4
,
we have that
p
(
1
)
=
0
.
Therefore, we can factorize it further and get
z
3
−
3
z
2
+
6
z
−
4
=
(
z
−
1
)
(
z
2
−
2
z
+
4
)
=
(
z
−
1
)
(
(
z
−
1
)
2
+
3
)
.
Their roots are just
z
1
=
1
,
z
2
=
1
+
i
√
3
,
z
3
=
1
−
i
√
3
.
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Similar questions
Q.
Write down complex numbers in the form of
A
+
i
B
.
1
+
2
i
+
3
i
2
1
−
2
i
+
3
i
2
.
Q.
Find the modulus of
1
+
2
i
1
−
3
i
Q.
Let
z
=
∣
∣ ∣
∣
1
1
+
2
i
−
5
i
1
−
2
i
−
3
5
+
3
i
5
i
5
−
3
i
7
∣
∣ ∣
∣
, then
Q.
let
z
=
∣
∣ ∣
∣
1
1
+
2
i
−
5
i
1
−
2
i
−
3
5
+
3
i
5
i
5
−
3
i
7
∣
∣ ∣
∣
then
Q.
Find the modulus and amplitude of
1
+
2
i
1
−
3
i
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