Find the zeros of the function below algebraically, if any exist. $f ( x ) = 2 x ^ { 4 } + 10 x ^ { 2 } + 12$
A) $- \sqrt { 3 } , - \sqrt { 2 } , \sqrt { 2 }$, and $\sqrt { 3 }$
B) $- \sqrt { 3 } , 0$, and $\sqrt { 3 }$
C) $- \sqrt { 3 }$ and $\sqrt { 3 }$
D) $- \sqrt { 2 }$ and $\sqrt { 2 }$
E) No zeros exist.

Question

Quizplus · Accepted Answer

The given function is a quartic polynomial that does not factor into real roots easily. By applying substitution methods or attempting to factor, it becomes apparent that the polynomial does not have real zeros that match any of the provided options.

Find the Zeros of the Function Below Algebraically, If Any f(x)=2x4+10x2+12f ( x ) = 2 x ^ { 4 } + 10 x ^ { 2 } + 12f(x)=2x4+10x2+12

Find the Zeros of the Function Below Algebraically, If Any $f ( x ) = 2 x ^ { 4 } + 10 x ^ { 2 } + 12$