for each zero state number of its multiplicity
x=-5
x=3/2
The term "zero state number" is not commonly used in mathematical or physical contexts. It's possible that you are referring to the term "zero" or "root" in terms of functions or equations.
Multiplicity refers to the number of times a particular root (zero) of a polynomial equation occurs. When you're given specific roots like x=-5 and x=3/2, each of them may be a root of some polynomial equation.
For example, let's say we have a polynomial function in the form f(x) = (x + 5)(2x - 3)^n, where n is a non-negative integer. In this example:
- The root x = -5 has a multiplicity of 1 because it occurs only once in the factor (x + 5).
- The root x = 3/2 (which is the solution to 2x - 3 = 0) would have a multiplicity equal to n, because the factor (2x - 3) occurs n times in the polynomial. The number of times it is repeated in factors of the polynomial determines its multiplicity.
Without additional context or a specific polynomial, it is impossible to give the exact multiplicity of these roots. Each would have a multiplicity of at least 1 by being roots, but how many times they are repeated (their multiplicity) would depend on the given polynomial equation they are roots of.