When you factor using the zero product rule, the solutions to the simpler equations are also the solutions to the original equation.

A.True
B. False

Question

When you factor using the zero product rule, the solutions to the simpler equations are also the solutions to the original equation.

A.True
B. False

anonymous · Answer

Yes usually, this is why you factor and set each factor equal to 0. In some circumstances though, you can occasionally get a solution to the simplified equations that doesn't work in the original, these are extraneous solutions.

anonymous · Answer

is it true of false

anonymous · Answer

True, usually.

anonymous · Answer

Thank you it was correct

whpalmer4 · Answer

@vinnv226 can you give an example of one of these extraneous solutions?  The set of roots and factors should always be a 1:1 mapping with no extraneous solutions.

whpalmer4 · Answer

If you have done some manipulation such that you square both sides of the equation, that can introduce extraneous solutions...

anonymous · Answer

If you have a polynomial without any fractional exponents, you don't expect any extraneous solutions. But especially with square roots and other even roots you have solutions that are extraneous. I guess it depends on the scope of the problem. The problem wasn't very specific so I'm assuming a wider scope.

whpalmer4 · Answer

polynomials don't have fractional exponents, by definition...

whpalmer4 · Answer

and even so, the extraneous solutions come because you introduced them by your manipulation, not because they existed there in the original.

anonymous · Answer

True, but extraneous solutions can happen in a multi step problem from your manipulation. I think we need to be careful about telling people that 100% of the time you factor something, the solutions to the factored equations will work in the original. It's better to get used to checking your solutions to make sure you don't have any extraneous ones.

whpalmer4 · Answer

agree 110% with checking work for the possibility of extraneous solutions (especially when doing problems where math is being used to simulate a real-life situation such as the path of a ball thrown from a building), but suggesting that there isn't a 1:1 mapping between the factors and the roots is incorrect.  

The question asked: when using the zero product rule, the solutions to the simpler equations are also solutions of the original equation.  That's 100% true.  What you do with those solutions is another matter :-)

anonymous · Answer

Ok, I definitely see your point. I guess I interpreted the question in a broader sense.