Question 1410b

Complex Numbers
2010 Paper 2 Question 1 Variant

Question

(a)
Solve the equation x28x+25=0.{x^2 - 8 x + 25=0.}
[2]
(b)
One root of the equation
x4x3x2+ax+b=0,x^4 - x^3 - x^2 + ax + b=0,
where a{a} and b{b} are real, is x=2+3i.{x=- 2 + 3 \mathrm{i}.}
Find the values of a{a} and b{b} and the other roots.
[5]

Answer