 Chapter 4

The Binomial Equation The case where a = 0 has obvious solution and therefore it is not considered in this chapter.

4.1 The binomial equation were x and a real numbers

A)    Consider the equation .
This equation has exactly one positive solution: , according to the definition of the root of a
non negative number. The equation does not have any negative solutions because for it is .
Therefore the equation has a unique solution, that is .
In general:

 The equation with v being an odd number and a>0, has exactly one solution: For example:

• • B)    Consider the equation Thinking like before we conclude that the equation has one positive solution: We observe though that  the number solves the equation as well.
So, the equation has two exactly solutions which are: In general:

 The equation with v even and a>0 has exactly two solutions, which are: For example:
• • C)    Lets consider the equation It is obvious that this equation has no solutions in R, since as we know for every x in R.
In general:

 The equation with v even and a<0 has no solutions in R.
For example:
• The equations  .
D)    Consider the equation I have  In general:

 The equation with v odd and a<0 has exactly one solution: For example:
• •       