Find a polynomial of least degree with only real coefficients and having the given zeros.
-$- \sqrt { 3 } , \sqrt { 3 }$, and $- 4 \mathrm { i }$
A) $f ( x ) = x ^ { 4 } + 13 x ^ { 2 } - 48$
B) $f ( x ) = x ^ { 4 } + 26 x ^ { 2 } + 48$
C) $f ( x ) = x ^ { 4 } - 26 x ^ { 2 } + 48$
D) $f ( x ) = x ^ { 4 } - 13 x ^ { 2 } - 48$

Question

Quizplus · Accepted Answer

Given the zeros $-\sqrt{3}, \sqrt{3},$ and $-4i$, we must also include the conjugate of the complex zero, $4i$, to ensure real coefficients. The factors corresponding to these zeros are $x + \sqrt{3}, x - \sqrt{3}, x + 4i,$ and $x - 4i$. Multiplying these factors gives the polynomial $f(x) = (x^2 - 3)(x^2 + 16) = x^4 + 13x^2 - 48$.

Find a Polynomial of Least Degree with Only Real Coefficients −3,3- \sqrt { 3 } , \sqrt { 3 }−3​,3​

Find a Polynomial of Least Degree with Only Real Coefficients $- \sqrt { 3 } , \sqrt { 3 }$