What is a function with a simple zero?

Question

Any examples of simple zeros and examples of non-simple zeros

Answer 1

If there is only one root at that value. For example (x - 2)(x - 4) = 0 has 2 simple zeroes at x= 2 and x=4.
Non-simple zeroes are called multiple zeroes like (x - 2)(x - 4)^3 = 0 where x=3 is not simple anymore. It has multiplicity of 3.

Answer 2

Simple Zero

Answer 3

In a more general way and also applicable to non algebraic equations, if the derivative exists," a "is is simple root of
f(x)=0 if f(a)=0 and f´(a) is not zero