Form a polynomial f(x) with real coefficients having the given degree and zeros.
-Degree: 5; zeros: 2, $- 3 \mathrm { i }$, and $4 - \mathrm { i }$
A) $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } + 26 x ^ { 3 } - 124 x ^ { 2 } + 72 x + 306$
B) $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } + 42 x ^ { 3 } - 124 x ^ { 2 } + 297 x - 306$
C) $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } - 42 x ^ { 3 } - 124 x ^ { 2 } + 297 x + 306$
D) $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } + 26 x ^ { 3 } - 124 x ^ { 2 } - 72 x - 306$

Question

Quizplus · Accepted Answer

The zeros are 2, -3i, and 4 - i. The complex zeros occur in conjugate pairs, so the other zero is 4 + i. The polynomial with these zeros is:$$f(x) = (x - 2)(x + 3i)(x - 4 + i)(x - 4 - i)$$$$= (x - 2)(x^2 + 9)(x^2 - 8x + 17)$$$$= x^5 - 10x^4 + 26x^3 - 124x^2 + 72x + 306$$

Form a Polynomial F(x) with Real Coefficients Having the Given −3i- 3 \mathrm { i }−3i

Form a Polynomial F(x) with Real Coefficients Having the Given $- 3 \mathrm { i }$