Find a polynomial function with real coefficients that the given zeros. $- 5 , - 5,1 + \sqrt { 3 } i$
A)Answers will vary. Sample answer: $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 9 x ^ { 2 } - 10 x + 100$
B)Answers will vary. Sample answer: $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 9 x ^ { 2 } - 10 x - 100$
C)Answers will vary. Sample answer: $f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 9 x ^ { 2 } - 10 x + 100$
D)Answers will vary. Sample answer: $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } - 9 x ^ { 2 } - 10 x + 100$
E)Answers will vary. Sample answer: $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 9 x ^ { 2 } + 10 x + 100$

Question

Quizplus · Accepted Answer

Given the zeros $-5, -5, 1 + \sqrt{3}i$, the polynomial must also include the conjugate $1 - \sqrt{3}i$ to ensure real coefficients. The factors corresponding to these zeros are $(x + 5), (x + 5), (x - (1 + \sqrt{3}i)), (x - (1 - \sqrt{3}i))$. Multiplying these factors yields a polynomial with real coefficients, and the sample answer in choice A correctly reflects a polynomial that could be generated from these zeros.

Find a Polynomial Function with Real Coefficients That the Given −5,−5,1+3i- 5 , - 5,1 + \sqrt { 3 } i−5,−5,1+3​i

Find a Polynomial Function with Real Coefficients That the Given $- 5 , - 5,1 + \sqrt { 3 } i$