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Discarding Unrealistic Negative Solutions in Applications
When a word problem that translates into a quadratic equation is solved algebraically, the factoring process may produce two solutions — including a negative value. In some real-world contexts, a negative answer does not make sense (for example, a length, a count of objects, or an elapsed time cannot be negative). When this happens, the negative solution is a valid algebraic answer to the equation but must be discarded because it does not fit the situation described in the problem. This is why the Check step in the problem-solving strategy requires more than verifying the algebra: the solver must also confirm that each answer is reasonable within the original real-world context. Not every quadratic application produces unrealistic negatives — for instance, a problem about the product of two consecutive integers may yield both a positive and a negative pair that are both meaningful.
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