Question 155144: How many solutions exist for a quadratic equation? How do we determine whether the solutions are real or complex?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
A quadratic polynomial can have 2 real solutions, 1 real solution, or 2 complex solutions. To determine whether the solutions are real or complex, simply use the discriminant formula.
For example, to see if the equation  has real or complex solutions, let's use the discriminant formula
From we can see that  ,  , and 
 Start with the discriminant formula.
 Plug in a=2, b=6, and c=-10
 Square 6 to get 36
 Multiply 4(2)(-10) to get (8)(-10)=-80
 Rewrite D=36--80 as D=36+80
 Add 36 to 80 to get 116
Since the discriminant is greater than zero, this means that there are two real solutions. So the quadratic has two real solutions
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