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My query concerns the number of roots of equations in which the powers of x are not integers (or rational numbers) but irrational numbers.

How, for instance, would one determine the total number of roots (real and complex) of this equation

x^(pi) + 3*(x^e)+x^8.99999-50*x = 100000 ? (e=2.71... pi=3.14....)

(The actual roots don't concern me, I am more interested in knowing how to determine, analytically, the total number of roots)

Many thanks for any advice.