HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems. The discriminant is the part of the quadratic equation under the radical, b2 − 4ac.The discriminate formula is b squared minus four ac for quadratic equation in standard form ax squared plus bx plus c. THE DISCRIMINANT The quantity under the radical in the quadratic formula, b 2-4 ac , is called the discriminant. You factor any square out and write it outside the root, if the discriminant is negative write an i i before the root. IXL's dynamic math practice skills offer comprehensive coverage of Pennsylvania high school standards. Find a skill to start practicing! Discriminant = 33; Nature of the Roots = The roots are real, distinct, and irrational 2. The three methods of solving quadratic equations are Factoring, Completing the Square, and the Quadratic Formula. Determine the value of the discriminant.