Why Real Function Sometimes have Imaginary Roots??

Question

According to my Professor at SDSU: "It just happens."

So we really have no clue why sometimes the roots of functions do not exist (meaning that they are imaginary roots not in the Real Number line)!!

Math is a human invention and we are Not perfect! Therefore Math can be flawed at times!! Even though all of our Technology and Sciences is solely based off of Math!!

Answer 1

Note that "real" numbers are no more "real" than "imaginary." They are both constructs.

One of several "reasons" is that the square of any "real" number is positive.

An example, x² + 2 = 0 → x² = -2, not possible with a "real" number. So we invent one (just like we invented "real" numbers). That number is i = √-1.

x² = -2

x² = (-1)(2)

x² = i √2