Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the
polynomial in standard form.
-2 (multiplicity 2) and $1 + 3 i$ (multiplicity 1 )
A) $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 40 x ^ { 2 } - 48 x + 40$
B) $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 22 x ^ { 2 } - 48 x + 40$
C) $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 22 x ^ { 2 } + 28 x + 40$
D) $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 22 x ^ { 2 } - 48 x + 40$

Question

Quizplus · Accepted Answer

The polynomial must have the zeros 2 (with multiplicity 2) and $1 + 3i$. Since the coefficients are real, the complex conjugate $1 - 3i$ must also be a zero. Thus, the polynomial is $(x-2)^2(x-(1+3i))(x-(1-3i))$, which simplifies to the polynomial in option D.

Write a Polynomial Function of Minimum Degree with Real Coefficients 1+3i1 + 3 i1+3i

Write a Polynomial Function of Minimum Degree with Real Coefficients $1 + 3 i$