Discriminant Practice Test

Calculate D=b²-4ac and use its sign and square status to classify quadratic roots and graph intersections.

Discriminant Practice Test

20 varied discriminant questions with worked explanations.

About This Discriminant Practice Test

For ax²+bx+c=0, the discriminant D=b²-4ac determines whether the quadratic has two real roots, one repeated real root, or no real roots. When D is positive, its square status also distinguishes rational roots from irrational roots for rational coefficients.

This test combines numerical calculation with interpretation. Questions ask for D, √D, root counts, x-intercepts, repeated-root formulas, classifications, and discriminants after an equation has first been rearranged into standard form.

Discriminant Skills Covered

You will identify coefficients including zero or negative values, calculate D accurately, interpret positive, zero, and negative cases, distinguish perfect-square and nonsquare positive values, connect roots with x-intercepts, and use D inside the quadratic formula.

How to Approach the Questions

  1. Rewrite the equation in ax²+bx+c=0 form before reading coefficients.
  2. Preserve the sign of b and c when substituting into b²-4ac.
  3. Classify the result by sign, then check whether a positive D is a perfect square.
  4. Use D=0 for a repeated root and D<0 for no real x-intercepts.

Common Mistakes to Avoid

Common errors include using b instead of b², losing the sign of a negative c, forgetting the factor 4, reading coefficients before moving all terms to one side, claiming every positive D gives rational roots, and confusing D with √D.

Practice Format

Use this free 20-question test for Algebra 1, Algebra 2, quadratic review, ACT-style preparation, tutoring, or independent study.