Find the zeros of the polynomial function and state the multiplicity of each.
$f ( x ) = 9 x ^ { 6 } + x ^ { 4 }$
A) $\left. 0 \text { (multiplicity } 4 ) , \pm \frac { 1 } { 3 } \text { (multiplicity } 1 \right)$
B) $0 \text { (multiplicity } 4 \text { ), } \frac { 1 } { 3 } \mathrm { i } \text { (multiplicity } 1 \text { ) }$
C) $1 \text { (multiplicity } 4 \text { ), } - \frac { 1 } { 3 } \mathrm { i } \text { (multiplicity } 1 \text { ) }$
D) $0 \text { (multiplicity } 4 \text { ), } \pm \frac { 1 } { 3 } \mathrm { i } \text { (multiplicity } 1 \text { ) }$

Question

Quizplus · Accepted Answer

The polynomial can be factored as $x^4(9x^2 + 1)$. The zero $x = 0$ has multiplicity 4, and the zeros of $9x^2 + 1 = 0$ are $x = \pm \frac{1}{3}i$, each with multiplicity 1.

Find the Zeros of the Polynomial Function and State the Multiplicity