Find all real solutions of the equation

How do you find all the solutions of an equation?

To solve for , you must first combine the ‘s on the right side of the equation. This will give you . Then, subtract and from both sides of the equation to get . Finally, divide both sides by to get the solution .

What does find all real solutions mean?

Frequently, in Algebra class, you will be called to find all “real solutions” of an equation. Such questions essentially are asking you to find all solutions of an equation, and should any imaginary solutions (containing the imaginary number ‘i’) come up, to discard these solutions.

What is a real solution in math?

A real solution in algebra is simply a solution to an equation that is a real number.

Is 0 a real number?

Real numbers consist of zero (0), the positive and negative integers (-3, -1, 2, 4), and all the fractional and decimal values in between (0.4, 3.1415927, 1/2). Real numbers are divided into rational and irrational numbers.

How do you find no solution?

Summary. If the equation ends with a false statement (ex: 0=3) then you know that there’s no solution. If the equation ends with a true statement (ex: 2=2) then you know that there’s infinitely many solutions or all real numbers.

Is 0 0 infinite or no solution?

For an answer to have an infinite solution, the two equations when you solve will equal 0=0 . If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions. For an answer to have no solution both answers would not equal each other.

How do you find three solutions of an equation?

To find three solutions to this equation, substitute three different numbers and calculate the result for y : Set x=0. y=9x−4 becomes: y=(9⋅0)−4. y=9−4. y=5. The first solution is: (0,5) Set x=10. y=9x−4 becomes: y=(9⋅10)−4. y=90−4. y=86. The second solution is: (10,86) Set x=−10.

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What is not a real number?

Non-real numbers are numbers that contain a square root of a negative number. Typically, the square root of -1 is denoted as “i”, and imaginary numbers are expressed as a multiple of i. Real numbers are all rational and irrational numbers which include whole numbers, repeating decimals and non-repeating decimals.

How do you tell if a quadratic has no solution?

If you get a positive number, the quadratic will have two unique solutions. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.

Can real solutions be negative?

It is not specific to trigonometry, any equation can have ‘real’ and/or ‘non real’ roots (solutions). They can be thought as being positive or negative, integer, fractional, rational or irrational multiples of the unit of the ‘real’ numbers, the number 1.

What is an equation with no solution?

The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. If you substitute these values into the original equation, you’ll see that they do not satisfy the equation.

How do you know if an equation has two solutions?

The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it’s less than 0, there are no solutions. If it’s equal to 0, there is one solution.

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