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 + 3i

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 + 3i

anonymous · Answer

(x-4) (x+8)    (x-(2+3i)) (x-(2-3i))
(x^2+4x-32)  (4x^2+9)

=4x^4+16x^3-119x^2+36x-288

anonymous · Answer

Remember factors including imaginary come in pairs so if you have 2i you must also have -2i, factor form it would be (x-2i)(x+2i)

anonymous · Answer

f(x) = x4 - 6x3 + 12x2 - 90x + 416

 f(x) = x4 - 45x2 + 180x - 416

 f(x) = x4 - 35x2 + 180x - 416

 f(x) = x4 - 6x3 - 12x2 + 90x - 416 @ehuman

anonymous · Answer

those are your possible answers?

anonymous · Answer

Yes @ehuman

anonymous · Answer

I obviously made a mistake.
Here are your 4 factors
(x-4) (x+8)    (x-(2+3i)) (x-(2-3i))
Foil them to find expanded solution.

anonymous · Answer

can you help me do that?

anonymous · Answer

@ehuman

anonymous · Answer

Apologies, I've worked it a couple different ways and don't come up with any of your choices. I must be rusty doing something wrong.

anonymous · Answer

Aww):