Table of Contents
Table of Contents
"Exercises of Equations and Disequations"
INTRODUCTION
SECOND DEGREE EQUATIONS AND POLYNOMIALS
EQUATIONS OF DEGREE HIGHER THAN THE SECOND
RATIONAL INEQUATIONS
IRRATIONAL EQUATIONS AND INEQUATIONS
EQUATIONS AND INEQUATIONS WITH THE MODULUS
"Exercises of Equations and Disequations"
"Exercises of Equations and Disequations"
SIMONE MALACRIDA
In this book, exercises are carried out regarding the following mathematical topics:
second-degree and higher-degree equations
rational inequalities
irrational equations and inequalities
equations and inequalities with the modulus
Initial theoretical hints are also presented to make the performance of the exercises understood
Simone Malacrida (1977)
Engineer and writer, has worked on research, finance, energy policy and industrial plants.
ANALYTICAL INDEX
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INTRODUCTION
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I – SECOND DEGREE EQUATIONS AND POLYNOMIALS
Exercise 1
Exercise2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
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II – EQUATIONS OF DEGREE HIGHER THAN THE SECOND
Exercise 1
Exercise or 2
Exercise 3
Exercise 4
Exercise 5
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III - RATIONAL INEQUATIONS
Exercise 1
Exercise 2
Exercise 3
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IV - IRRATIONAL EQUATIONS AND INEQUATIONS
Exercise 1
Exercise 2 _
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
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V - EQUATIONS AND INEQUATIONS WITH THE MODULE
Exercise 1
Exercises or 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
INTRODUCTION
INTRODUCTION
In this exercise book, some examples of calculation relating to elementary equations and inequalities of an algebraic nature are carried out.
The equations and inequalities of second degree and higher degree which can be traced back to the first through Ruffini's theorem will be addressed. In addition, an overview of rational, irrational and absolute value equations and inequalities will be given.
The resolution of these equations is the basis of any mathematical competence of a certain level and, therefore, it is essential baggage for those who are preparing to face the final three years of high school.
In order to understand in more detail what is explained in the resolution of the exercises, the theoretical context of reference is recalled at the beginning of each chapter.
What is exposed in this workbook is generally addressed in the second year of high school.
I
SECOND DEGREE EQUATIONS AND POLYNOMIALS
SECOND DEGREE EQUATIONS AND POLYNOMIALS
A quadratic equation has the generic form given by:
We immediately see that if a=0 the equation of second degree is actually of first degree and everything is reduced to the case of the previous chapter.
If instead a is different from zero, the solutions are as follows:
In the set of real numbers, there can be three distinct cases based on the value of 
.
If this value is negative, it is seen that there are no solutions in the set of real numbers and the equation is therefore impossible .
If this value is greater than zero there are two real and distinct solutions .
Finally, if it is equal to zero there are two coincident real solutions equal to:
On the basis of the values of b and c, special cases can be determined for the solutions.
If b and c are equal to zero, the equation is called monomial and has two solutions that coincide at x=0.
If b=0 but c is different from zero, the equation is said to be pure and has two solutions given by:
Obviously the root must be positive to have definite solutions, vice versa it means that the equation is impossible.
If, on the other hand, c=0 and b is different from zero, the equation is said to be spurious .
One solution of the spurious equation is always x=0, the other solution is:
Exercise 1
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Impressum
Verlag: BookRix GmbH & Co. KG
Tag der Veröffentlichung: 21.04.2023
ISBN: 978-3-7554-3975-2
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