1. anonymous

2. steve816

"showing all your working" Wow, that's some atrocious grammar right there!

3. anonymous

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

4. Owlcoffee

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.

5. anonymous

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

6. Owlcoffee

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.

7. anonymous

okay thank you.. i can do the rest