For the Polynomial, List Each Real Zero and Its Multiplicity $$f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x - 3 )$$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
- $$f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x - 3 )$$

A) 0 , multiplicity 4 , touches $x$ -axis;
3 , multiplicity 1 , touches $x$ -axis
$\sqrt { 3 }$ , multiplicity 1 , crosses $x$ -axis;
$- \sqrt { 3 }$ , multiplicity 1 , crosses $x$ -axis

B) 0, multiplicity 4 , crosses $x$ -axis;
3 , multiplicity 1 , crosses $x$ -axis;

C) 0 , multiplicity 4 , crosses $x$ -axis;
3 , multiplicity 1 , touches $x$ -axis;
$\sqrt { 3 }$ , multiplicity 1 , touches $x$ -axis;
$- \sqrt { 3 }$ , multiplicity 1 , touches $x$ -axis

D) 0 , multiplicity 4 , touches $x$ -axis;
3 , multiplicity 1 , crosses $x$ -axis

Correct Answer:

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