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For solving a quadratic, you mean? Well, if you have real solutions you know that your quadratic has real numbers that make f(x) equal 0. For example, the quadratic f(x) = x^2 - x - 6 has -2 and 3 for solutions, because if you put in either of those two numbers for x, you get 0.

I don't know how far along in your math career you are, but there aren't really any quadratics with no solutions, just with no real solutions. Some quadratics require you to take the square root of a negative number to get a solution, which is acceptable, it's just not a real solution anymore.

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Q: What is the difference between a real number and a no solution answer?
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