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Yes, over the real set of numbers. For example, the graph of y=x2+1 is a regular parabola with a vertex that is one unit above the origin. Because the vertex is the lowest point on the graph, and 1>0, there is no way for it to touch the x-axis.

NOTE: But if we're considering imaginary numbers, the values "i" and "-i" would be the zeroes. I'm pretty sure that all polynomial functions have a number of zeroes equal to their degree if we include imaginary numbers.

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