SOLUTION: 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 + 8i AND Stat

Question 765031: 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 + 8i

AND
State how many imaginary and real zeros the function has.
f(x) = x^4 - 8x^3 + 17x^2 - 8x +16
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
All complex roots (zeroes) come in PAIRS. You need to include 2 - 8i as one of the four zeroes. Then we have the factored form of the polynomial is
(1)
Just FOIL the first two factor and FOIL the last factors to get
(2)
Now multiply the two quadratics of (2) and get
(3)
This function (3) has two real zeroes, 7 and -11 and a complex pair of zeroes, 2+8i and 2-8i
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