(i)[2]
Determine $m$.
(ii(a))[5]
Therefore, showing all of your working, determine the three roots of the equation $p(z) = 0$.
(ii(b))[6]
Hence, showing all of your working, find the six roots of the equation $p(z^2) = 0$.
Mathematics 9709 · AS & A Level · Complex numbers
Complex numbers — practice question
The polynomial $p(z)$ is given by $p(z) = z^3 + mz^2 + 24z + 32$, with $m$ a constant. You are told that $(z + 2)$ divides $p(z)$.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $p(-2)=0$, or an equivalent condition, to work out $m$.” …
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