Question

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

Answer 1

Suppose we have a generic polynomial of the form:
 $ax ^ 2 + bx + c$
 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.
 Answer:
 You must observe the term of the polynomial with greater exponent.

Answer 2

The degree of polynomial is equivalent to the number of roots a polynomial has.

The Linear Factorization Theorem states that a polynomial of degree n has exactly n linear factors, and each can be written in the form (x - c) , where c is a root.

There are two types of roots. The real root and the complex root.