Form a polynomial f(x) with real coefficients having the given degree and zeros.
-Degree: 4 ; zeros: $2 \mathrm { i }$ and $- 5 \mathrm { i }$
A) $f ( x ) = x ^ { 4 } + 29 x ^ { 2 } + 100$
B) $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 29 x ^ { 2 } + 100$
C) $f ( x ) = x ^ { 4 } + 29 x ^ { 2 } - 5 x + 100$
D) $f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 100$

Question

Quizplus · Accepted Answer

Given the zeros $2i$ and $-5i$, their conjugates $ -2i $ and $ 5i $ are also zeros because the coefficients of the polynomial are real. The factors corresponding to these zeros are $x - 2i$, $x + 2i$, $x + 5i$, and $x - 5i$. Multiplying these factors in pairs gives $(x^2 + 4)(x^2 + 25)$, which simplifies to $x^4 + 29x^2 + 100$.

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

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