Chapter
5
Polynomial
Equations of the Second Degree
5.1
The equation where
a,b,c belong in R, and a is not equal to 0
We are going to solve
the quadratic equation as it is called with the help of an algorithm.
We have:
If we set then
the last equation becomes:
(1)
Now we have the following possibilities:

If D>0 then (1).
That means that the equation has two different
solutions.

If D=0 then (1).
In this instance we say that the equations has
one double root.

If D<0 then (1) has
no solutions in R, that is the equation has no real roots.
If we consider the equation in the set of complex numbers C we have:
(1)
.
So
the equation has two solutions that are complex numbers.