Question

Write the polynomial of the smallest degree with roots i, -i, 4i, and -4i.
I think the answer is:
x^4 + 16x^2
I just want to confirm
Thank you!

Answer 1

you have got root 0!

Answer 2

What do you mean by that?

Answer 3

there is no root i and -i in your polinomial. but there is one 0.

Answer 4

Oh, so should it be x^4 + 0x^3 + 16x^2 ?

Answer 5

no. there is again one root zero.

if you want polynomial with root i and -i: (x^2+1), -i and i are solutions of equation x^2+1=0

Answer 6

do you know what roots of polynomial are?

Answer 7

Yes, it's the same thing as the zeroes.

Answer 8

so whats the root of polynomial (x^2+16)

Answer 9

x square root 2 - 16

Answer 10

no. when is \[x^2+16=0\]?

Answer 11

idk