It is possible for a sixth-degree polynomial to have only one zero?why?

Answer 1

no. the number of roots or zeros is equal to the highest degree of the polynomial.

even something like y = (x - 6)^6, which is a 6th degree polynomial with all its zeros at x = 6 it is still considered to have 6 of those zeros all equal to x = 6.

Answer 2

Sure.

F(x) = x^6 is an example. So is G(x) = (x-1)^2 * (x^4 +1).

Well, G(x) is an example over the real numbers but not over the complex numbers. F(x) is an example everywhere.

Answer 3

Yes; y = x^6 has only one zero, namely x = 0.

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