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Do all rational equations have solutions?

Updated: 1/10/2023
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11y ago

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No. They can just as well have zero solutions, several solutions, or even infinitely many solutions.

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Vivianne Schamberger

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1y ago
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Q: Do all rational equations have solutions?
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Related questions

Do all rational equations have a single solution?

Not all rational equations have a single solution but can have more than one because of having polynomials. All rational equations do have solutions that cannot fulfill the answer.


Do all rational equations have one solution?

No. They can just as well have zero solutions, several solutions, or even infinitely many solutions.


Do all rational numbers have single solution?

Numbers are numbers, not questions or equations. They do not have solutions.


What is the solution of rational equations reducible to quadratic?

They are the solutions for the reduced quadratic.


What are the solutions of rational algebraic equations?

They can be rational, irrational or complex numbers.They can be rational, irrational or complex numbers.They can be rational, irrational or complex numbers.They can be rational, irrational or complex numbers.


What are 3 real rational solutions to this system of equations z equals x squared y equals z squared x equals y squared?

The two rational solutions are (0,0,0) and (1,1,1). There are no other real solutions.


Why is factoring a valuable tool for solving quadratic equations?

In some simple cases, factoring allows you to find solutions to a quadratic equations easily.Factoring works best when the solutions are integers or simple rational numbers. Factoring is useless if the solutions are irrational or complex numbers. With rational numbers which are relatively complicated (large numerators and denominators) factoring may not offer much of an advantage.


What is the difference with equations with integers and equations with rational numbers?

It is a trivial difference. If you multiply every term in the equation with rational numbers by the common multiple of all the rational numbers then you will have an equation with integers.


What is equations that have the same solutions?

Simultaneous equations have the same solutions.


How do carpenters use rational equations?

They use rational equations for fun in the evening to relax.


How can you find out how many solutions an equation has?

By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.


How do you answer equations?

The answers to equations are their solutions