SOLUTION: (i) How many solutions exist for a quadratic equation? Explain. (ii) How do we determine whether the solutions are real or complex?

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Question 35898: (i) How many solutions exist for a quadratic equation? Explain.
(ii) How do we determine whether the solutions are real or complex?
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
The solutions for quadratic equations vary. You can have either one or two answers. To find the type of answer, think of the discriminant in this equation: x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ where x is the solutions to the quadratic equation: ax%5E2%2Bbx%2Bc=0. The discriminant is sqrt%28+b%5E2-4%2Aa%2Ac+%29. If the discriminant is greater than zero and is a perfect square, you have two rationl, real roots. If the discriminant is greater than zero and is not a perfect square, then you have two real, irrational roots. If the discriminant is equal to zero, you have one real, rational root. Last, if the discriminant is less than zero, you have two complex roots.