As with most advanced math, if your "real life" involves engineering work, you will use such math; otherwise, you will hardly have anything to do, in this case, with polynomial functions.
In the real domain, yes. In the complex domain, no.
Yes, but in this case, the coefficients of the polynomial can not all be real.
A power function is of the form xa where a is a real number. A polynomial function is of the form anxn + an-1xn-1 + ... + a1x + a0 for some positive integer n, and all the ai are real constants.
Yes, a polynomial can have no rational zeros while still having real zeros. This occurs, for example, in the case of a polynomial like (x^2 - 2), which has real zeros ((\sqrt{2}) and (-\sqrt{2})) but no rational zeros. According to the Rational Root Theorem, any rational root must be a factor of the constant term, and if none exist among the possible candidates, the polynomial can still have irrational real roots.
Yes, that's the same thing.
That depends on what you mean with "real-life". You won't need polynomial functions to sell stuff at a supermarket, or to cut off a dead branch from your tree... but if you work in science and engineering, you will need some really advanced math - much more than a simple polynomial function.
In the real domain, yes. In the complex domain, no.
Yes, but in this case, the coefficients of the polynomial can not all be real.
A power function is of the form xa where a is a real number. A polynomial function is of the form anxn + an-1xn-1 + ... + a1x + a0 for some positive integer n, and all the ai are real constants.
No, In real life days vampired no not exist
niga
nods limbs doesn't exist in real life!!
No, all Sonic characters are fictional, and don't exist in real life.
Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)
Either one made to function with blanks only or something made up that doesn't exist in real life.
1+x2 is a polynomial and doesn't have a real root.
Wizards do not exist in real life.