Zer0, Roots and x-intercept. What's Their Relationship???

After I learned the Chapter 2.3, the question of "what's the difference and relationship between zero, root, and x-intercept?" pop in my mind. Why do they have different names yet they are almost the same????? Weird right? :P


Then. I found out they are actually interrelated and they are same in terms of its value.
Let's say for example the graph below.
 
The x-intercept on the graph is the zero of the graph and the polynomial equation; the zero of the graph is the factor of the polynomial equation; the x-intercept and zero are the roots of the polynomial equation. Thus, the zero, roots and x-intercepts are -1 and 5 (as from the graph above). 


BUT, this is only for those polynomial equation that is factorable. For those polynomial equation that are not factorable, we can find out their zero or roots or x-intercept (if they have roots), we need to use the quadratic formula 

or by using our graphing calculator.


Therefore, as a conclusion:

• the real roots of a polynomial equation P(x)=0 is similar to the x-intercept of the graph P(x) and vice versa.
• A factorable polynomial equation's roots are equal to its zero and thus solving the factor of it.
• BUT, when we come to polynomial equation that is not factorable, we need to solve it using technology or by using graphing method. 

Web resources: Wikipedia, "Zero of a Function" <http://en.wikipedia.org/wiki/Zero_of_a_function>

                        
The Math Page, "The Roots, or Zeros, of a Polynomial"          <http://www.themathpage.com/aprecalc/roots-zeros-polynomial.htm>