Find the zeros of the polynomial function and state the multiplicity of each.
-$4 x ^ { 7 } + x ^ { 5 }$
A) 0 (multiplicity 5), $\pm \frac { 1 } { 2 } \mathrm { i }$ (multiplicity 1 )
B) 0 (multiplicity 5), $\frac { 1 } { 2 } \mathrm { i }$ (multiplicity 1 )
C) 1 (multiplicity 5), $- \frac { 1 } { 2 } \mathrm { i }$ (multiplicity 1 )
D) 0 (multiplicity $5 ), \pm \frac { 1 } { 2 }$ (multiplicity 1 $)$

Question

Quizplus · Accepted Answer

The polynomial can be factored as $x^5(4x^2 + 1)$. The zeros are $x = 0$ with multiplicity 5 (from $x^5$) and $x = \pm \frac{1}{2}i$ (from $4x^2 + 1 = 0$, solving gives $x^2 = -\frac{1}{4}$).

Find the Zeros of the Polynomial Function and State the Multiplicity