(a)[2]
Show that $(x + 3)$ divides $p(x)$.
(b)[3]
Show that $z = -1 + 2\sqrt{6}i$ is one root of $p(z) = 0$.
(c)[7]
Hence find the complex numbers $z$ that are roots of $p\left(z^2\right) = 0$.
Mathematics 9709 · AS & A Level · Complex numbers
Complex numbers — practice question
The polynomial $x^3 + 5x^2 + 31x + 75$ is represented by $p(x)$.