Find the zeros of the function below algebraically, if any exist.
$$f ( x ) = 25 x ^ { 3 } - 60 x ^ { 2 } + 36 x$$
A) $- \frac { 6 } { 5 }$ and 0
B) 0 and $\frac { 6 } { 5 }$
C) $- \frac { 6 } { 5 } , 0$, and $\frac { 6 } { 5 }$
D) $- \frac { 6 } { 5 }$ and $\frac { 6 } { 5 }$
E) No zeros exist.

Question

Quizplus · Accepted Answer

First, factor out the greatest common factor, which is $x$, giving $x(25x^2 - 60x + 36)$. Further factoring the quadratic gives $x(5x - 6)^2$, indicating zeros at $x = 0$ and $x = \frac{6}{5}$.

Find the Zeros of the Function Below Algebraically, If Any f(x)=25x3−60x2+36xf ( x ) = 25 x ^ { 3 } - 60 x ^ { 2 } + 36 xf(x)=25x3−60x2+36x

Find the Zeros of the Function Below Algebraically, If Any $f ( x ) = 25 x ^ { 3 } - 60 x ^ { 2 } + 36 x$