finding the equation given the roots

i thought i forgot how to do the "proper" method for part b so i'll reverse what you do to get the roots in the first place

$z=2\pm 4i[br][br]z-2=\pm 4i[br][br](z-2)^2=-16[br][br](z-2)^2 +16=0[br][br](z^2 -4z+4)+16=0[br][br]p=-4[br]q=20$

i thought i forgot how to do the "proper" method for part b so i'll reverse what you do to get the roots in the first place

$z=2\pm 4i[br][br]z-2=\pm 4i[br][br](z-2)^2=-16[br][br](z-2)^2 +16=0[br][br](z^2 -4z+4)+16=0[br][br]p=-4[br]q=20$

That's a perfectly fine method. The other is expanding $(z - (2-4i))(z - (2 + 4i)) = z^2 - z(2-4i + 2 + 4i) + (2-4i)(2+4i)$

Looks fine, but the "proper" method would be the sum/product of roots formulae:

$-p=\alpha +\beta = -\frac{b}{a}, q= \alpha \beta = \frac{c}{a}$

which give the same results.

what is this? i've never seen this before :/ should i know this for fp1?

The sum and product of roots appears on the IAL specification for Edexcel Further Mathematics AS (F1), but not for the Edexcel GCE Further Mathematics AS (FP1). Not sure about other boards.

It is on FP1 for all boards, including Edexcel (UK) FP1.

I'm afraid not. Here are the first two chapters from the IAL F1 specification.



The second chapter is not anywhere to be found on the FP1 GCE specification as shown below.



And I can confirm after doing all FP1 papers and F1 papers, nothing about $\alpha$ and $\beta$ roots has ever come up in an FP1 paper, only F1.

Can't say about other boards though.