Question 412670
Please help me with determining the number of real solutions based on the discriminate. 

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 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

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If the discriminant:

b^2-4ac>0. then the equation has two distinct real roots.  You can see this from the figure above . If the discriminate turns out to be a perfect square, you probably could factor the equation to determine the roots
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b^2-4ac=0, then the equation has one real root, called a double root. You can see this from the figure above, the root would be equal to -b/2a
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b^2-4ac>0, Then the equation has no real roots. You would still, however, have two nonreal or imaginary complex number roots, because you are taking the sqrt of a negative number.