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

Question

Quizplus · Accepted Answer

The real zeros are $-\frac{1}{4}$ with multiplicity 4, and $-1$ with multiplicity 5. A zero with even multiplicity means the graph touches the x-axis, and a zero with odd multiplicity means the graph crosses the x-axis.

For the Polynomial, List Each Real Zero and Its Multiplicity f(x)=(x+14)4(x+1)5f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }f(x)=(x+41​)4(x+1)5

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