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According to the Zero Product Rule the solutions to the simpler equations are also the solutions to the original equation. A.True B.False?
Wiki User
∙ 7y ago
The statement is true.
Wiki User
∙ 7y ago
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When you factor using the Zero Product Rule the solutions to the simpler equations are also the solutions to the original equation?
True yal :)
Why do you have to check the solutions when you have to solve radical equations?
Checking your solution in the original equation is always a good idea,simply to determine whether or not you made a mistake.If your solution doesn't make the original equation true, then it's wrong.
How do you solve radicals in math?
That depends on the type of problem. For example, if you have equations involving radicals, it often helps to square both sides of the equation. Note that when you do this, you may introduce additional solutions, which are not solutions to the original equation.
What do you call the solution of a equation derived from an original equation that is not a solution of the original equation?
That's an extraneous solution. You need to check for these when algebraically solving equations, especially when you take both sides of an equation to a power.
Why do you check your answers for rational equations and radical equations?
You plug the number back into the original equation. If you have a specific example, that would help.
When you factor using the Zero Product Rule the solutions to the simpler equations are also the solutions to the original equation?
True yal :)
What happens if you are checking a solution for the radical expression and find that it makes one of the denominators in the expression equal to zero?
Then it is not a solution of the original equation. It is quite common, when solving equations involving radicals, or even when solving equations with fractions, that "extraneous" solutions are added in the converted equation - additional solutions that are not solutions of the original equation. For example, when you multiply both sides of an equation by a factor (x-1), this is valid EXCEPT for the case that x = 1. Therefore, in this example, if x = 1 is a solution of the transformed equation, it may not be a solution to the original equation.
When you factor using the zero product rule the solutions to the simpler equations are also the solutions to the original equation true or false?
True - otherwise there would be no point in doing it!
Why is it necessary to check for extraneous solutions in radical equations?
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.
Why do you have to check the solutions when you have to solve radical equations?
Checking your solution in the original equation is always a good idea,simply to determine whether or not you made a mistake.If your solution doesn't make the original equation true, then it's wrong.
What reasoning and explanations can be used when solving radical equations?
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.
How do you find all real solutions to the system of equations 4x 2 plus y 2 equals 100 and 4x 2 minus y 2 equals 62?
Add the two equations together. This will give you a single equation in one variable. Solve this - it should give you two solutions. Then replace the corresponding variable for each of the solutions in any of the original equations.
How do you solve radicals in math?
That depends on the type of problem. For example, if you have equations involving radicals, it often helps to square both sides of the equation. Note that when you do this, you may introduce additional solutions, which are not solutions to the original equation.
What do you call the solution of a equation derived from an original equation that is not a solution of the original equation?
That's an extraneous solution. You need to check for these when algebraically solving equations, especially when you take both sides of an equation to a power.
When solving a rational equation why is it necessary to perform a check?
It is important to check your answers to make sure that it doesn't give a zero denominator in the original equation. When we multiply both sides of an equation by the LCM the result might have solutions that are not solutions of the original equation. We have to check possible solutions in the original equation to make sure that the denominator does not equal zero. There is also the possibility that calculation errors were made in solving.
In general when solving a radical equation should you first isolate the radical and then both sides?
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.
Why do you check your answers for rational equations and radical equations?
You plug the number back into the original equation. If you have a specific example, that would help.
