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Question 1410b
Complex Numbers
2010 Paper 2 Question 1 Variant
Question
Generate new
(a)
Solve the equation
x
2
−
4
x
+
5
=
0.
{x^2 - 4 x + 5=0.}
x
2
−
4
x
+
5
=
0.
[2]
(b)
One root of the equation
x
4
+
11
x
3
+
54
x
2
+
a
x
+
b
=
0
,
x^4 + 11 x^3 + 54 x^2 + ax + b=0,
x
4
+
11
x
3
+
54
x
2
+
a
x
+
b
=
0
,
where
a
{a}
a
and
b
{b}
b
are real, is
x
=
−
3
+
3
i
.
{x=- 3 + 3 \mathrm{i}.}
x
=
−
3
+
3
i
.
Find the values of
a
{a}
a
and
b
{b}
b
and the other roots.
[5]
Answer
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