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

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

Step-by-step 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)