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Unformatted text preview: ct that they are real, nor will it change the fact that they are different. 2. A double root. We will get this solution set if b 2 - 4ac = 0 . Here we will be taking the square root of zero, which is zero. However, this means that the “plus or minus” part of the numerator will be zero and so the numerator in the quadratic formula will be –b. In other words, we will get a single real number out of the quadratic formula, which is what we get when we get a double root. 3. Two complex solutions. We will get this solution set if b 2 - 4ac < 0 . If the discriminant is negative we will be taking the square root of negative numbers in the quadratic formula which means that we will get complex solutions. Also, we will get two since they have a “plus or minus” in front of the square root. So, let’s summarize up the results here. 1. If b 2 - 4ac > 0 then we will get two real solutions to the quadratic equation. 2. If b 2 - 4ac = 0 then we will get a double root to the quadratic equation. 3. If b 2 - 4ac < 0 then we will get two complex solutions...
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