Solve the following quadratic equation (for commerce student)
x² – (5-i) x + (18+i) = 0
Answers
Answered by
2
Explanation:
We apply the Quadratic Formula and get,
x
=
(
5
−
i
)
±
√
(
5
−
i
)
2
−
4
(
18
+
i
)
2
,
i
.
e
.
,
x
=
(
5
−
i
)
±
{
(
25
−
10
i
−
1
)
−
72
−
4
i
}
2
,
or
,
x
=
(
5
−
i
)
±
√
−
48
−
14
i
2
,
∴
x
=
(
5
−
i
)
±
i
√
48
+
14
i
2
...
...
...
...
...
...
...
...
.
.
(
⋆
)
.
So, to find
x
,
we need to find
√
48
+
14
i
.
Let,
u
+
i
v
=
√
48
+
14
i
;
u
,
v
∈
R
.
∴
(
u
+
i
v
)
2
=
u
2
+
2
i
u
v
−
v
2
=
48
+
14
i
.
Comparing the Real & Imaginary Parts, we have,
u
2
−
v
2
=
48
,
and
,
u
v
=
7
.
Now,
(
u
2
+
v
2
)
2
=
(
u
2
−
v
2
)
2
+
4
u
2
v
2
=
48
2
+
14
2
=
50
2
,
∴
u
2
+
v
2
=
50
...
(
1
)
,
and
,
u
2
−
v
2
=
48
...
(
2
)
.
(
1
)
+
(
2
)
,
&
,
(
1
)
−
(
2
)
give,
u
=
7
,
v
=
1
.
∴
√
48
+
14
i
=
7
+
i
.
Finally, from
(
⋆
)
,
we get,
x
=
(
5
−
i
)
±
i
(
7
+
i
)
2
,
i
.
e
.
,
x
=
2
+
3
i
,
or
,
x
=
3
−
4
i
,
are the desired roots!
Enjoy Maths.!
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