SOLUTION: How do you know if a quadratic equation will have one, two, or no sloution?

Question 569254: How do you know if a quadratic equation will have one, two, or no sloution?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
All quadratics will have two (complex) solutions. However, to determine if they're real or if there are duplicate roots, you'll have to take the discriminant, defined as delta = b^2 - 4ac.

Recall the quadratic formula

If b^2 - 4ac > 0, then the square root will be defined and you will have two real solutions.

If b^2 - 4ac = 0, then the square root will be equal to 0, and you'll have a duplicate root (-b/2a).

If b^2 - 4ac < 0, then the square root will be a complex number and you'll have two complex solutions (by complex, I mean Im(x) is not equal to 0).
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