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## Main Question or Discussion Point

I am doing some independent study and appreciate that a polynomial (in x) of integer degree (n) can have at most n roots; many proofs to this effect exist.

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.

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.