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

-$$f ( x ) = 5 ( x - 4 ) ( x - 6 ) ^ { 3 }$$
A)4, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis
B)-4, multiplicity 1, crosses x-axis; -6, multiplicity 3, crosses x-axis
C)-4, multiplicity 1, touches x-axis; -6, multiplicity 3
D)4, multiplicity 1, touches x-axis; 6, multiplicity 3

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.

-$$f ( x ) = 5 ( x - 4 ) ( x - 6 ) ^ { 3 }$$
A)4, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis
B)-4, multiplicity 1, crosses x-axis; -6, multiplicity 3, crosses x-axis
C)-4, multiplicity 1, touches x-axis; -6, multiplicity 3
D)4, multiplicity 1, touches x-axis; 6, multiplicity 3

Quizplus · Accepted Answer

The zeros of the polynomial are x = 4 with multiplicity 1 and x = 6 with multiplicity 3. A zero with an odd multiplicity will always result in the graph crossing the x-axis at that point.

Determine the Real Zeros of the Polynomial and Their Multiplicities f(x)=5(x−4)(x−6)3f ( x ) = 5 ( x - 4 ) ( x - 6 ) ^ { 3 }f(x)=5(x−4)(x−6)3

Determine the Real Zeros of the Polynomial and Their Multiplicities $f ( x ) = 5 ( x - 4 ) ( x - 6 ) ^ { 3 }$