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In the real domain, yes. In the complex domain, no.
no a plynomial can not have more zeros than the highest (degree) number of the function at leas that is what i was taught. double check the math.
A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.
Try the quadratic formula. X = -b ± (sqrt(b^2-4ac)/2a)
No. It would not be a polynomial function then.