Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

8, -14, and 3 + 9i

Answer 1

This is gonna be a pain.
You polynomial will have to be in this form if those are going to be the zeros:
(x - 8)(x + 14)(x - (3 + 9i))(x - (3 - 9i))
Notice that if 3 + 9i is zero, the conjugate 3 - 9i must also be a zero
And, yes, you will have to expand all of that out to get it in standard form.
yuck!

Answer 2

like foil?

Answer 3

yeah

Answer 4

i'm seeing if i can do it on my super duper TI calculator right now.

Answer 5

Do you have a TI calculator with an "expand()" function?

Answer 6

ok. but how would you foil (x-(3+9i)

Answer 7

i dont think so i have a ti-84

Answer 8

Go to wolframalpha.com and type:
expand (x - 8)(x + 14)(x - (3 + 9i))(x - (3 - 9i))
or just copy paste that in

Answer 9

ok thank you

Answer 10

Let me know if that works for you.
It gives you a polynomial result with no i's (they cancel when you expand)

Answer 11

it says f(x) = x4 - 58x2 + 1212x - 10,080

Answer 12

That's correct.
It would be a pain to get that by hand. You get a bunch of i^2 and i^4...but they go away since i^2 is -1 and i^4 is just 1.

Answer 13

oh ok! thank you so much!

Answer 14

No problem!