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The key is the expression in the square root

# The key is the expression in the square root - The key is...

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The key is the expression in the square root: . In general there are three cases: 1. is positive. The square root of a positive number is also some positive number. So in the numerator of the quadratic formula we will get two values: (-b + the square root) and (-b - the square root). So when we get two solutions. 2. is zero. The square root of zero is zero. So in the numerator we get (-b + 0) and (-b - 0). But both of these are equal to -b! So when we only get one solution. 3. is negative. And what is the square root of a negative number? What can we square and get a negative number as an answer? Answer: Nothing. You cannot square any Real number and get a negative. So when there are no solutions. 2. Finding the equation from the solution(s) One way to find solutions from the equation is to factor it. For example, solving we factor it: For a product to be zero one of the factors must be zero. In other "words": x-2 = 0 or x-3 =0 Solving these we get:

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x=2 or x=3 Now what you want is to be able to do this in reverse. Well all the steps above are reversible. Therefore, if we have two solutions:
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The key is the expression in the square root - The key is...

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