Question

please help
question in comments.. medal and fan

Answer 1

"showing all your working"

Wow, that's some atrocious grammar right there!

Answer 2

@steve816 if you can't help,, be sure to get lost :)
this is an examination question of Cambridge paper..

Answer 3

Well, I would suggest you first find the roots of the function:
\[p(z)=z^3+6z^2+24z +32\]
Then it'll make the work of \(p(z^2)\) much easier.

Answer 4

yes already done that.. it was a part of the question.. ive got \[z=2 , z=-2+2\sqrt{3}i, z=-2-2\sqrt{3}i\]

Answer 5

Good, that's corect, in a factorized form it would look like:
\[p(z)=(z-2)(z^2 + 4z +16)\]
And now, if we want to find the roots of \(p(z^2)\) we will just use that form:
\[p(z^2)=(z^2-2)(z^4+4z^2+16)\]
You can use ruffinis division to factor out that 4th degree polynomial and make it into a 3rd degree.

Answer 6

okay thank you.. i can do the rest