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Equations of the form y2 = x3 + ax + b are powerful mathematical tools. The Birch and Swinnerton-Dyer conjecture tells how to determine how many solutions they have in the realm of rational numbers-information that could solve a host of problems, if the conjecture is true.

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What is a infinite rational numbers?

There is no infinite rational number. There are infinitely many of them but that is not the same.


How can you determine whether a polynomial equation has imaginary solutions?

To determine whether a polynomial equation has imaginary solutions, you must first identify what type of equation it is. If it is a quadratic equation, you can use the quadratic formula to solve for the solutions. If the equation is a cubic or higher order polynomial, you can use the Rational Root Theorem to determine if there are any imaginary solutions. The Rational Root Theorem states that if a polynomial equation has rational solutions, they must be a factor of the constant term divided by a factor of the leading coefficient. If there are no rational solutions, then the equation has imaginary solutions. To use the Rational Root Theorem, first list out all the possible rational solutions. Then, plug each possible rational solution into the equation and see if it is a solution. If there are any solutions, then the equation has imaginary solutions. If not, then there are no imaginary solutions.


Are infinite numbe rationals?

Yes. There are infinite whole numbers, and whole numbers are rational.


How many rational numbers are there between 0.2and0.3?

There is an infinite number of them between any two rational numbers.


What is the states that an infinite number of rational numbers can be found between any two rational numbers?

That is the property of infinite density of rational numbers. If x and y are any two rational numbers then w = (x + y)/2 is a rational number between them. And then there is a rational number between x and w. This process can be continued without end.

Related Questions

If 2a equals b and a and b are both cubes then what numbers are a and b?

If a and b are both rational then a = 0 = b. If they are not both rational then there are an infinite number of solutions.


What is a infinite rational numbers?

There is no infinite rational number. There are infinitely many of them but that is not the same.


List of rational and irrational numbers?

-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.


How meny rational numbers are there?

There are an infinite number of them.


How can you determine whether a polynomial equation has imaginary solutions?

To determine whether a polynomial equation has imaginary solutions, you must first identify what type of equation it is. If it is a quadratic equation, you can use the quadratic formula to solve for the solutions. If the equation is a cubic or higher order polynomial, you can use the Rational Root Theorem to determine if there are any imaginary solutions. The Rational Root Theorem states that if a polynomial equation has rational solutions, they must be a factor of the constant term divided by a factor of the leading coefficient. If there are no rational solutions, then the equation has imaginary solutions. To use the Rational Root Theorem, first list out all the possible rational solutions. Then, plug each possible rational solution into the equation and see if it is a solution. If there are any solutions, then the equation has imaginary solutions. If not, then there are no imaginary solutions.


Are infinite numbe rationals?

Yes. There are infinite whole numbers, and whole numbers are rational.


Rational numbers between -1 and 3?

There are an infinite number of rational numbers between any two rational numbers.


What is An infinite number of rational numbers can be found between any two rational numbers?

yes it can


Are There are fewer rational numbers then irrational numbers?

Yes, there are countably infinite rationals but uncountably infinite irrationals.


Is 12 5 a rational of irrational?

It is a rational number. An irrational number is a decimal that is infinite and has no repition or pattern.


Is the square root of 35 rational or not?

It is Irrational. If you have an infinite number of decimals that doesn't have a specific pattern, then it is rational!


How many rational numbers are there between 0.2and0.3?

There is an infinite number of them between any two rational numbers.