In the previous examples of this
chapter, every time we ended up with an equation of the form ax+b=0 where
a and b were specific numbers. We could instantly then see in which case
of the table in paragraph 3.1 our equation corresponded.

This is not valid though if the coefficients
a,b are presented with the help of letters. In this case these letters
are called parameters. Solving equations with parameters is a little more
harder.

__Example 1__

Solve for the various
values of the equation
.

__Solution__

The equation can be solved as follows:

**(1)**

We have the following possibilities:

**A) **If and
then

**B) **If then
(1)0x= -1 which
does not have a solution in R

**C) **If
then (1)0x=0
which is true for every

__Example 2__

Prove that for the every value of the parameters
a,b the equation bellow has solution:

__Solution__

**(1)**

Now we have the following possibilities:

**A) **If then
(1) has unique solution and that is:

**B) **If a+b=0
then (1) becomes 0x=0 which has infinitive number of solutions

That means that in every case the equation has a solution.

__Exercise 1__

For the various values of the parameters , solve the equation: