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# Extraneous Solutions to Real Life Problems

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The answer was finding the length and width of a rectangle. The results were x= 3 and x= -4. Neither the length or width can be a negative number. However, 3 did work in the original equation."

You are correct that in a real world physical problem like you cited the answer cannot be negative.

But is the negative answer "extraneous" according to the mathematical definition? Please explain in 2 paragraphs.

The above question must be answered. The question originated from the question below which was already answered: What are extraneous solutions of an equation? Why do they sometimes occur in the process of solving rational or radical equations?

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#### Solution Preview

According to the fundamental theorem of algebra, a polynomial equation of nth degree has n solutions, be they real, imaginary, repetitive, distinct or any combination of these. Therefore, if an equation is quadratic, i.e., of the second degree, it will invariably have two solutions, whether or no they are admissible in a real world situation. Similarly, if the ...

#### Solution Summary

Extraneous Solutions to Real Life Problems are discussed. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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