Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the
x-axis at each zero.

-$$f ( x ) = 3 ( x - 2 ) ( x - 6 ) ^ { 4 }$$
A)-2, multiplicity 1, touches x-axis; -6, multiplicity 4, crosses x-axis
B)2, multiplicity 1, touches x-axis; 6, multiplicity 4, crosses x-axis
C)-2, multiplicity 1, crosses x-axis; -6, multiplicity 4, touches x-axis
D)2, multiplicity 1, crosses x-axis; 6, multiplicity 4, touches x-axis

Question

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the
x-axis at each zero.

-$$f ( x ) = 3 ( x - 2 ) ( x - 6 ) ^ { 4 }$$
A)-2, multiplicity 1, touches x-axis; -6, multiplicity 4, crosses x-axis
B)2, multiplicity 1, touches x-axis; 6, multiplicity 4, crosses x-axis
C)-2, multiplicity 1, crosses x-axis; -6, multiplicity 4, touches x-axis
D)2, multiplicity 1, crosses x-axis; 6, multiplicity 4, touches x-axis

Quizplus · Accepted Answer

The zeros of the polynomial are $x = 2$ with multiplicity 1 and $x = 6$ with multiplicity 4. A zero with an odd multiplicity will cross the x-axis, while a zero with an even multiplicity will touch the x-axis.

Determine the Real Zeros of the Polynomial and Their Multiplicities f(x)=3(x−2)(x−6)4f ( x ) = 3 ( x - 2 ) ( x - 6 ) ^ { 4 }f(x)=3(x−2)(x−6)4

Determine the Real Zeros of the Polynomial and Their Multiplicities $f ( x ) = 3 ( x - 2 ) ( x - 6 ) ^ { 4 }$