Question

Write a polynomial equation of the smallest degree with roots -4i, 4i, and 2

Answer 1

the smallest degree would be the product of these binomials: (x-4i)(x+4i)(x-2)

just multiply these out...

Answer 2

(x+4i)(x-4i) Start off with the pair of complex numbers getting a real simple result then multiply that simple result with the (x-2)

Answer 3

I think I got to
(x^2-4ix+4ix+i^2)(x-2)
But I don't know what to do after

Answer 4

Real close, you will see that the "4ix" cancel as one is positive the other negative. But when you multiplied 4i times 4i you should of gotten -16i^2\[-16i ^{2}\] Now an important question: Do you know what \[i ^{2}\] is equal to?

Answer 5

i^2=-1

Answer 6

Yes very good so the result of (x+4i)(x-4i) should give you the final result of :\[x ^{2}+16\]Do you follow that?

Answer 7

so x^2 +16 is the answer? Or is there more to the answer?

Answer 8

No you are not done you have to this :
\[(x-2)(x ^{2}+16)\]

Answer 9

x^3-2x^2+16x-32?

Answer 10

That is a good Bingo.

Answer 11

Thank you so much.

Answer 12

You're very welcome.