Question

write polynomial function with given roots:
2i and - square root 2

Answer 1

\[-\sqrt{2}\]

Answer 2

@jim_thompson5910

Answer 3

@Mertsj help plzz :/

Answer 4

Now remember...if 2i is a root, then -2i is also a root. Furthermore is -sqrt2 is a root then +sqrt2 is also a root. Does that help?

Answer 5

yes but how would i set it up i already have that part set

Answer 6

Do you know that if x=3 is a root then x-3 is a factor?

Answer 7

So if x = 2i is a root then x-2i is a factor.
So your equation must be:
\[(x-2i)(x+2i)(x-\sqrt{2})(x+\sqrt{2})=0\]

Answer 8

Which in simpler form is :
\[(x^2+4)(x^2-2)=0\]

Answer 9

ok and if you dont do it in simpler form do i have to set it to zero

Answer 10

Which is the same as:
\[x^4+2x^2-8=0\]

Answer 11

yes

Answer 12

Or you could write f(x)= because the directions say to write a polynomial function.

Answer 13

ok and then i guess thats where i have to start working it out

Answer 14

So If you just write the factors like I did and multiply them out you will get f(x)=x^4+2x^2-8 and that is your answer.

Answer 15

oh ok thanks

Answer 16

yw