Question 1410b

Complex Numbers
2010 Paper 2 Question 1 Variant

Question

(a)
Solve the equation x210x+29=0.{x^2 - 10 x + 29=0.}
[2]
(b)
One root of the equation
x42x3+12x2+ax+b=0,x^4 - 2 x^3 + 12 x^2 + ax + b=0,
where a{a} and b{b} are real, is x=14i.{x=- 1 - 4 \mathrm{i}.}
Find the values of a{a} and b{b} and the other roots.
[5]

Answer