Question

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

4, -8, and 2 + 5i

Answer 1

so, you need three zeros? I ask because it's hard to setup a polynomial with 2+5i as a root. If it was 4, -8, 2, and 5i it would be easier.

Answer 2

Yeah i know its kind of strange, but that is what my homework is asking for

Answer 3

Would I start setting up the conjugates of the given zeros? so it would be (x-4) (x+8) and (2-5i)?

Answer 4

yes, that's right.

Answer 5

Then multiply the three conjugates together?

Answer 6

Yes, multiply the conjugates to start

Answer 7

If a polynomial has one complex root: (2 + 5i) then it will also have the complex conjugate (2 - 5i) as the root.

Answer 8

ok. I multiplied (x-4) (x+8) and got x^2+4x-32. I'm having a problem trying to multiply it with (2-5i).

Answer 9

you can't without having non-rational coefficients

Answer 10

you need a conjugate (x^2 - (2+5i)^2))

Answer 11

Complex roots always occur in pairs. So multiply [ x - (2 + 5i) ] and [ x - (2 - 5i) ]
You will get a quadratic equation and the i will go away.
Multiply that by (x - 4)(x + 8)

Answer 12

Your answer will be a fourth degree polynomial.

Answer 13

Thank you guys so much! Couldn't solve it without you guys!

Answer 14

glad to be able to help.