To calculate the discriminant of a quadratic equation, put the equation in standard form. Substitute the coefficients from the equation into the formula b^2-4ac. The value of the discriminant indicates what kind of solutions that particular quadratic equation possesses.
- Put the quadratic equation in standard form
In standard form, a quadratic equation has all the coefficients and variables placed on the left side of the equal sign, with only the number 0 remaining on the right side of the equal sign. Order the terms so that the variables with the highest exponents are farthest to the left. A quadratic equation in standard form has this basic format: ax^2 + bx +c = 0.
- Substitute the coefficients from the equation into the formula b^2-4ac
Once the quadratic equation is in standard form, the coefficients are already in the order a, b, c, so it is easy to substitute them into the formula for the discriminant. For example, if the quadratic equation in standard form is 4x^2 + 3x + 1 = 0, then a = 4, b = 3 and c = 1. The discriminant formula with the appropriate values substituted is 3^2 - 4*4*1.
- Find the discriminant by evaluating the formula
To find the discriminant, evaluate the formula with the coefficient values substituted. In the example from Step 2, 3^2-4*4*1 = 9-16 = -7. The discriminant is -7. A negative discriminant tells you the quadratic equation has two complex solutions. A positive discriminant indicates two real solutions. A discriminant of 0 indicates one real solution.