Mat 117 wk 7 DQ 1 - 1. How to determine the number of...

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1. How to determine the number of solutions. Let's look at the quadratic formula: 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":
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Mat 117 wk 7 DQ 1 - 1. How to determine the number of...

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