Find a polynomial of least degree with only real coefficients and having the given zeros.
-$- \sqrt { 6 } , \sqrt { 6 }$, and $- 7$ (multiplicity 2 )
A) $f ( x ) = x ^ { 4 } + 14 x ^ { 3 } + 43 x ^ { 2 } - 84 x - 294$
B) $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 6 x + 42$
C) $f ( x ) = x ^ { 4 } - 14 x ^ { 3 } - 43 x ^ { 2 } + 84 x + 294$
D) $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 6 x - 42$

Question

Quizplus · Accepted Answer

Given the zeros $-\sqrt{6}, \sqrt{6}$, and $-7$ (with a multiplicity of 2), the polynomial can be constructed by multiplying the factors associated with each zero: $(x + \sqrt{6})(x - \sqrt{6})(x + 7)^2$. Simplifying this expression leads to a polynomial of degree 4 with real coefficients, matching option A.

Find a Polynomial of Least Degree with Only Real Coefficients −6,6- \sqrt { 6 } , \sqrt { 6 }−6​,6​

Find a Polynomial of Least Degree with Only Real Coefficients $- \sqrt { 6 } , \sqrt { 6 }$