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.
No, In real life days vampired no not exist
nods limbs doesn't exist in real life!!
"The Force" doesn't exist in real life.
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, all Sonic characters are fictional, and don't exist in real life.
Wizards do not exist in real life.
No one. They are not real and do not exist.
1+x2 is a polynomial and doesn't have a real root.