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What is a quadratic polynomial which has no zeros?
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.
Is it possible that the polynomial function doesn't have zeros?
In the real domain, yes. In the complex domain, no.
What is rational algebra expression?
Basically, a rational expression is one that can be written as one polynomial, divided by another polynomial.
How does my knowledge of polynomial function prepare me to understand rational function?
A rational function is the quotient of two polynomial functions.
What about rational functions creates undefined and asymptotic behavior?
A rational function is the ratio of two polynomial functions. The function that is the denominator will have roots (or zeros) in the complex field and may have real roots. If it has real roots, then evaluating the rational function at such points will require division by zero. This is not defined. Since polynomials are continuous functions, their value will be close to zero near their roots. So, near a zero, the rational function will entail division by a very small quantity and this will result in the asymptotic behaviour.
