Question

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

4, -2, and -1 + 2i

Answer 1

@geerky42 @geerky42

Answer 2

Help!

Answer 3

@genius12

Answer 4

(x-4)(x+2)(x - (-1 + 2i) ) = (x-4)(x+2)(x + 1 - 2i)

We want a polynomial function with real coefficients, so multiply it by ( (x+1) +2i )

(x-4)(x+2)(x + 1 - 2i) )(x - 1 + 2i) = (x-4)(x+2)( (x+1)² - (2i)² ) = (x-4)(x+2)((x+1)² + 4)

Now expand it. Is this clear?

Answer 5

Wait, so what is the final answer? I got x^4-2x^3-3x^2-10x-40, but that is not one of the four choices that is given. @geerky42

Answer 6

Is \(x^4-7 x^2-26 x-40\) one of the options?

Answer 7

@mangnagelytis

Answer 8

Oh, I see my error. It is one of the choices. Thank you!

Answer 9

Glad I helped. You understand it, right?

Answer 10

Yes.

Answer 11

Good, lol.