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.

        (1)
 
 
 
 .

        So the equation has two solutions that are complex numbers.

      

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