Zeros of cubic functions

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Andrei B. Alexandra

Mathematics                                                                                                                                

Zeros of Cubic Functions

I am going to investigate the zeros of a cubic function. Zeros of functions are in other words roots of functions. A cubic function might have a root, two roots or three roots. An easy way to find the roots of a function is by using the Remainder Theorem, which states that a is a root of  if and only if. I will make a very god use of this Theorem troughout the essay.

My mission is to find the equation of the tangent lines to the average of two of the three roots, by  taking the roots two at a time. Then to find where the tangent line intersect the curve again in order to be able to state a conjecture concerning the roots of the cubic function and the tangent line at the average value of these roots.

Let us consider the cubic function  and take a look at the graph of it:

                                                                                                     

                     

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First I will state the roots of the function as follow

  • -3.0
  • -1.5
  •  1.5

And then prove this using the Remainder Theorem:

 is a root of

Substituting x with the values of the roots:

           

           

           

           

     

     

Verification on the calculator :

The next step will be to find ...

This is a preview of the whole essay