Form a polynomial f(x)with real coefficients having the given degree and zeros.
-Degree: 4 ; zeros: $2 \mathrm { i }$ and $- 4 \mathrm { i }$
A) $f ( x ) = x ^ { 4 } - 4 x ^ { 2 } + 64$
B) $f ( x ) = x ^ { 4 } + 20 x ^ { 2 } - 4 x + 64$
C) $f ( x ) = x ^ { 4 } + 20 x ^ { 2 } + 64$
D) $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 20 x ^ { 2 } + 64$

Question

Quizplus · Accepted Answer

The polynomial must have conjugate pairs of zeros, so the zeros are $2i, -2i, 4i, -4i$. The polynomial is $(x^2 + 4)(x^2 + 16) = x^4 + 20x^2 + 64$.

Form a Polynomial F(x)with Real Coefficients Having the Given Degree 2i2 \mathrm { i }2i

Form a Polynomial F(x)with Real Coefficients Having the Given Degree $2 \mathrm { i }$