Which one of the following is a polynomial with real coefficients that has -2 and $2+i$ as zeros?
A) $(x+2)(x-2-i)$
B) $(x-2)(x+2+i)$
C) $(x+2)\left(x^{2}-4 x+5\right)$
D) $(x-2)\left(x^{2}-4 x+5\right)$
E) $(x+2)\left(x^{2}+5\right)$

Question

Which one of the following is a polynomial with real coefficients that has  -2  and $2+i$ as zeros?
A) $(x+2)(x-2-i)$
B) $(x-2)(x+2+i)$
C) $(x+2)\left(x^{2}-4 x+5\right)$
D) $(x-2)\left(x^{2}-4 x+5\right)$
E) $(x+2)\left(x^{2}+5\right)$

Quizplus · Accepted Answer

For a polynomial with real coefficients, complex roots must come in conjugate pairs. Since $2+i$ is a root, its conjugate $2-i$ must also be a root. The polynomial $(x+2)\left(x^{2}-4x+5\right)$ expands to include $2+i$ and $2-i$ as roots, along with $-2$, fulfilling the given conditions.

Which One of the Following Is a Polynomial with Real 2+i2+i2+i

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