Question

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

7, -11, and 2 + 6i

Answer 1

x^4 - 53x^2 + 468 - 3080

Explanation:

If 2+6i is a root, then so is 2-6i

So, if you want a leading coefficient of 1, we have

y = (x-7)(x+11)(x-(2+6i))(x-(2-6i))

= (x-7)(x+11)((x-2)-6i)((x-2)+6i)

= (x-7)(x+11)((x-2)^2 + 6^2)

= (x-7)(x+11)(x^2-4x+4+36)

= (x-7)(x+11)(x^2-4x+40)