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In a quadratic equation, the discriminant helps tell you the number of real solutions to a quadratic equation. In this tutorial, see how to find the discriminant of a quadratic equation and use it to determine the number of solutions!
1 Identify the form of the expression. 2  It is a quadratic trinomial with coefficients a = 1, b = 6, and c = â5. 3  Its discriminant is D = b 2 â 4 Â· a Â· c = 6 2 â 4 Â· 1 Â· (â5) = 56, which is not a perfect square so we must factor the expression using the completing the square method. If D is negative then the above formula contains the square root of a negative number. 2  Over the real numbers this is not allowed and means that the quadratic trinomial can't be factored, but over the complex numbers this is no problem. 3  This case is described in detail below. 4  Identify the form of the expression.