How can you quickly determine the number of roots a polynomial will have by looking at the equation?

Suppose we have a generic polynomial of the form:
 
 To know how many roots the polynomial can have, the first thing you should do is observe the term of greatest exponent.
 For this case, the term of greatest exponent is 2.
 Therefore, the polynomial has 2 roots.
 
 You must observe the term of the polynomial with greater exponent.

With a continuous thought process.