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It really depends on the type of equation. Sometimes you can know, from experience with similar equations. But in many cases, you have to actually do the work of trying to solve the equation.

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0A quadratic equation can have a maximum of 2 solutions. If the discriminant (b2-4ac) turns out to be less than 0, the equation will have no real roots. If the Discriminant is equal to 0, it will have equal roots. But, if the discriminant turns out to be more than 0,then the equation will have unequal and real roots.

With a negative discriminant, the two solutions are imaginary.

1) When solving radical equations, it is often convenient to square both sides of the equation. 2) When doing this, extraneous solutions may be introduced - the new equation may have solutions that are not solutions of the original equation. Here is a simple example (without radicals): The equation x = 5 has exactly one solution (if you replace x with 5, the equation is true, for other values, it isn't). If you square both sides, you get: x2 = 25 which also has the solution x = 5. However, it also has the extraneous solution x = -5, which is not a solution to the original equation.

None because without an equality sign the given expression is not an equation and so therefore no solutions are possible.

You can be certain if the equation is linear, that is, of the form ax + b = 0 where a and b are constants.

You can't really know that in all cases. But with some practice in working with equations, you'll start to notice certain patterns. For example, you'll know that certain functions are periodic, and that an equation such as: sin(x) = 0 have infinitely many solutions, due to the periodicity of the function. This one is easy; we can make some small changes: sin(2x + 3) = 0.5 Here it isn't as easy to guess the exact solutions of the equation, but due to our knowledge of the periodicity of the sine function, we can assume that it has infinitely many solutions. Another example: a single equation with two or more variables normally has infinitely many solutions, for example: y = 3x + 2

Yes and sometimes it can have more than one solution.

None because without an equal sign it's not an equation

None because without an equality sign it cannot be an equation

None because without an equality sign the given expression is not an equation.

Without an equality sign the given terms can't be considered to be an equation and so therefore no solutions are possible.

Without an equality sign the given expression can't be considered to be an equation and so therefore there are no solutions.

There are none because without an equality sign it can not be considered to be an equation and the + or - values of 3x and 10 are not given

The basic method is the same as for other types of equations: you need to isolate the variable ("x", or whatever variable you need to solve for). In the case of radical equations, it often helps to square both sides of the equation, to get rid of the radical. You may need to rearrange the equation before squaring. It is important to note that when you do this (square both sides), the new equation may have solutions which are NOT part of the original equation. Such solutions are known as "extraneous" solutions. Here is a simple example (without radicals): x = 5 (has one solution, namely, 5) Squaring both sides: x squared = 25 (has two solutions, namely 5, and -5). To protect against this situation, make sure you check each "solution" of the modified equation against the original equation, and reject the solutions that don't satisfy it.

None because without an equality sign the given terms can't be considered to be an equation.

None because without an equality sign the given terms can't be considered to be an equation.

quantitative problem solving skills means there is no single best answer that may be available. Without further information and context, there is no way to determine whether both solutions or all solutions are valid for that particular problem. ex--- x=4 and x=-4 are both solutions for x^2= 16.

Without an equality sign and not knowing the plus or minus value of 11 it can't be considered to be an equation.

None because without an equal it is not an equation. But if it was in the form of x2+7x+12 = 0 then it would have 2 solutions which are x = -3 and x = -4

None because without an equality sign the terms of the given expression is not an equation.

Without the inclusion of an equality sign and not knowing the plus or minus value of 80 the expression can not be considered to be an equation.But if you meant: 9x2-6x-80 = 0 then (3x+8)(3x-10) = 0 when factoredAnd its solutions are: x = -8/3 and x = 10/3

An equation can have zero solutions, one solution, two solutions, or many solutions. A solution is any number that, when replaced into the equation, will give an equality. An example of an equation without a solution is x = x + 1. No matter what number you use for "x", the right part will always be one more than the left part. Therefore, the equation has no solution. (Also, if you subtract "x" from each side, you get the equation 0 = 1, which is obviously false.)

None because without an equality sign it can't be considered to be an equation.

None because without an equality sign the given terms can't be considered to be an equation

In some cases, a knowledge of the function in question helps. For example, when you have multiple equations, if you have more equations than variables you will usually have infinite solutions. Another example is that certain functions are known to be periodic, for instance the trigonometric functions - so an equation such as sin(x) = 1/2 may have infinite solution, due to the periodicity.

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