9709/Oct Nov/33/2010/Q10

The polynomial p(z) is defined by

p(z) = z^3 + mz^2 + 24z + 32,

where m is a constant. It is given that (z + 2) is a factor of p(z).

(i) Find the value of m.

(ii) Hence, showing all your working, find

(a) the three roots of the equation p(z) = 0,

(b) the six roots of the equation p(z^2) = 0.

Solution:

Reference: PYQ - Oct/Nov 2010 Paper 33 Q10