Question

Find all zeros of ƒ(x)=x4–22x3+121x2.Then determine the multiplicity at each zero. State whether the graph will touch or cross the x-axis at the zero.

Answer 1

• 0, 11, both multiplicity 2
• touch, not cross, at each 0

Explanation:

The function factors as ...

f(x) = x^4 -22x^3 +121x^2

f(x) = x^2(x^2 -22x +121)

f(x) = x^2(x -11)^2

The zeros are x=0 and x=11, each of multiplicity 2.

Because the multiplicity is even, the graph will touch at each zero, not cross.