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.
Solve for the various
values of the equation
The equation can be solved as follows:
We have the following possibilities:
A) If and
B) If then (1)0x= -1 which does not have a solution in R
which is true for every
Prove that for the every value of the parameters
a,b the equation bellow has solution:
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.
For the various values of the parameters , solve the equation: