Find the zeros of the function and state the multiplicities.
-$m ( x ) = x ^ { 5 } - 3 x ^ { 3 }$
A) $- \sqrt { 3 } , 0 , \sqrt { 3 }$; each of multiplicity 3
B) $- \sqrt { 3 } , \sqrt { 3 }$ each of multiplicity 1 ; 0 of multiplicity 3
C) $- \sqrt { 3 } , \sqrt { 3 }$ each of multiplicity $3 ; 0$ of multiplicity 1
D) $- \sqrt { 3 } , 0 , \sqrt { 3 }$; each of multiplicity 1

Question

Quizplus · Accepted Answer

To find the zeros of the function $m(x) = x^5 - 3x^3$, we factor out the common term $x^3$, giving us $x^3(x^2 - 3)$. Setting each factor equal to zero gives us the zeros: $x = 0$ from $x^3 = 0$, and $x = \pm \sqrt{3}$ from $x^2 - 3 = 0$. The multiplicity of the zero at $x = 0$ is 3 because the factor $x^3$ appears once, and the multiplicities of the zeros at $x = \pm \sqrt{3}$ are 1 because the factor $x^2 - 3$ is a quadratic that does not repeat.

Find the Zeros of the Function and State the Multiplicities m(x)=x5−3x3m ( x ) = x ^ { 5 } - 3 x ^ { 3 }m(x)=x5−3x3

Find the Zeros of the Function and State the Multiplicities $m ( x ) = x ^ { 5 } - 3 x ^ { 3 }$