The discriminant is what distinguishes x1 from x2:If the discriminant is positive, (b2-4ac > 0) then x1 and x2 will have different values - 2 different solutions.If the discriminant is equal to zero (b2-4ac = 0), then x1=x2 =-b / 2a.The quadratic has only one solution.If the discriminant is negative (b2-4ac < 0), then the quadratic has no real solutions, since you can't take the square root of a negative number without resorting to imaginary numbers (which are thankfully not tested on the GMAT).Therefore, if a question asks for the number of solutions a quadratic has, plug in the values of a, b and c into the discriminant b2-4ac and find out whether it is positive, zero or negative.

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