Question 1410b

Complex Numbers
2010 Paper 2 Question 1 Variant

Question

(a)
Solve the equation x26x+25=0.{x^2 - 6 x + 25=0.}
[2]
(b)
One root of the equation
x413x3+71x2+ax+b=0,x^4 - 13 x^3 + 71 x^2 + ax + b=0,
where a{a} and b{b} are real, is x=4+3i.{x=4 + 3 \mathrm{i}.}
Find the values of a{a} and b{b} and the other roots.
[5]

Answer