For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$$f ( x ) = \frac { 1 } { 5 } x \left( x ^ { 2 } - 5 \right)$$
A) 0 , multiplicity 1

B) $\sqrt { 5 }$, multiplicity 1 , touches $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis

C) 0 , multiplicity 1 , crosses x-axis;
$\sqrt { 5 }$, multiplicity 1 , touches $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , crosses $x$-axis

D) 0 , multiplicity 1 , touches $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , crosses $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis

Question

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$$f ( x ) = \frac { 1 } { 5 } x \left( x ^ { 2 } - 5 \right)$$
A) 0 , multiplicity 1

B) $\sqrt { 5 }$, multiplicity 1 , touches $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis

C) 0 , multiplicity 1 , crosses x-axis;
$\sqrt { 5 }$, multiplicity 1 , touches $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , crosses $x$-axis

D) 0 , multiplicity 1 , touches $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , crosses $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis

Quizplus · Accepted Answer

The zeros of the polynomial are 0, $\sqrt{5}$, and $-\sqrt{5}$, each with multiplicity 1, indicating the graph crosses the x-axis at these points. The multiplicity being odd for each zero means the graph crosses the x-axis at each intercept.

For the Polynomial, List Each Real Zero and Its Multiplicity f(x)=15x(x2−5)f ( x ) = \frac { 1 } { 5 } x \left( x ^ { 2 } - 5 \right)f(x)=51​x(x2−5)

For the Polynomial, List Each Real Zero and Its Multiplicity $f ( x ) = \frac { 1 } { 5 } x \left( x ^ { 2 } - 5 \right)$