Question

What is the difference between a polynomial or rational equation and polynomial or rationl inequality?

Answer 1

An polynomial equation has an equality sign and, in the case of only 1 variable, it translates geometrically into a line.
f(x) =a0 + a1 x + a2 x^2 + ... an x^n

we could write y = a0 + a1 x + a2 x^2 + ... an x^n

An polynomial inequality has a greater than or less than sign and, in the case of only 1 variable, it translates geometrically into a surface.
y > a0 + a1 x + a2 x^2 + ... an x^n
y <= a0 + a1 x + a2 x^2 + ... an x^n
y >= a0 + a1 x + a2 x^2 + ... an x^n

In this case, we usually don't ewrite f(x) < , > etc, because it would have problems with the definition of function.