ROOTS OF POLYNOMIALS OF GRADES 2,3 AND 4

Introduction

More than 4,000 years ago the Babylonians had a "recipe" which allowed them to find solutions to certain quadratic equations of the type: x2 -bx=c. But it was not until almost a century later that the Arab mathematician Al-Jwârizmî developed the algebra of the polynomials; however, what application do the polynomials have in our daily life? Well, the polynomials are occupied in the field of construction since it makes it possible for us to find the area of a surface of a house.

Development 

Among all the mathematical operations that can be performed, such as addition, subtraction, multiplication and division, these polynomials have formulas to obtain the roots in their different grades 2,3,and 4.

The roots of a polynomial are the solutions of the equation that are obtained when the polynomial is equal to 0

When an equation is second degree it is solved with the formula 

On the other hand, if you have a third degree equation, it is solved by the Rufinni method

To carry out this operation we will call alpha to the root of the equation.

In Ruffini's scheme the only thing that will be done is to divide by x-a where a is the known root of polynomial.

In Ruffini's scheme the only thing that will be done is to divide by x-a where a is the known root of  polynomial.

 

On the other hand, to find the square root of a fourth degree equation there are several methods but the most useful and simple is to convert it to a second degree equation by means of factorization:

Conclusion

Knowing these different ways of solving a polynomial to obtain its roots is very useful, besides it facilitates learning in procedures; on the other hand we can realize that factoring in these is really important for the solution.  I consider that it is important to know the bases, its uses in the daily life to be able to use it in other scopes