Question

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

2, -4, and 1 + 3i

I remember doing this but i forget where to start?

Answer 1

There was a similar problem today. I just copied and pasted the previous answer.

To do this problem, we must realize that complex roots of a polynomial with real coefficients come in conjugates, i.e. in pairs like a+bi and a-bi.
So minimally, the polynomial must have the following roots:
8, -14, 3+9i and 3-9i.

To construct such a polynomial, we would proceed in writing down the polynomial in factored form, and then expand to get the polynomial in standard form.
For example, the polynomial having -2,3, 4-i, 4+i would be written down as:
y(x)=(x+2)(x-3)(x-4+i)(x-4-i)
which expands to:
\( x^4−9x^3+19x^2+31x−102\)
NOTE: This is NOT the answer to the given question, just an example.

Answer 2

OHHH! Ok Thanks, i knew it was something like that i just wasn't sure.