Question

Can someone explain multiplicity of a zero?

Answer 1

The multiplicity is the number of "times" a zero exists.

So, if the Function would be (x-3)(x-3)(x-1)=0
The zeros would be 3 (with a multiplicity of 2), and 1.

So any time you see the same factor more than once, it has a multiplicity greater than 1.

Answer 2

Multiplicity refers to the exponents of the factors.  For example:

x³(x + 1)(x + 2)²(x² + 1) = 0

x:        has a multiplicity of 3 because its exponent is 3

x + 1:    has a multiplicity of 1 because its exponent is 1:  (x + 1)¹

x + 2:    has a multiplicity of 2 because its exponent is 2

x² + 1:    has a multiplicity of 1 because its exponent is 1: (x² + 1)¹

Hope this helped!