Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 25 x$
A) $0,5 , - 5$
B) $0,5 , - 5$
C) $0,5 , - 5$
D) $5 , - 5$
E) $5 , - 5$

Question

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 25 x$ 
A) $0,5 , - 5$ 
B) $0,5 , - 5$ 
C) $0,5 , - 5$ 
D) $5 , - 5$ 
E) $5 , - 5$

Quizplus · Accepted Answer

From the graph, we can see that the function intersects the x-axis at x = 0, x = 5, and x = -5. To find the zeros algebraically, we can set the function equal to zero and factor out an x:

$x^3 - 25x = 0$
$x(x^2 - 25) = 0$
$x(x-5)(x+5) = 0$

This gives us the same zeros as the graph: x = 0, x = 5, and x = -5.

Select the Graph of the Function and Determine the Zeros f(x)=x3−25xf ( x ) = x ^ { 3 } - 25 xf(x)=x3−25x

Select the Graph of the Function and Determine the Zeros $f ( x ) = x ^ { 3 } - 25 x$