Skill: quadratic-formula

Quadratic Formula Practice

An endless supply of never-repeating quadratic formula problems with instant feedback. Solve equations, read the discriminant like a fortune-teller, and label a, b, c without sign slips — one problem at a time.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Solve with the formula

How to enter answers

Two solutions: separate them with a comma, like -2, -3 or 1/2, 3. Either order counts. Fractions like -2/3 and decimals like 0.5 are accepted.
No real solutions: type no real solutions (or none).
Discriminant: a single integer, like 25 or -4.
Number of real solutions: 0, 1, or 2.
Label a, b, c: three integers separated by commas, like 2, -7, 3.

2 What you’ll practice

Every problem is generated fresh from 10 templates across three question types — a problem never repeats until its whole pool is used up.

Solve with the formula

Label a, b, c, compute the discriminant, and solve. Integer roots, fraction roots, double roots, missing terms, and equations with no real solutions all appear.

2x² − 7x + 3 = 0 → x = 3 or x = 1/2

Discriminant detective

Compute b² − 4ac, or use it to predict how many real solutions an equation has — before doing any more work.

x² + 4x + 5 = 0 → D = −4, so 0 real solutions

Label a, b, c

Read the coefficients out of standard form with their signs — including the sneaky missing-term cases.

x² − 9 = 0 → a = 1, b = 0, c = −9

3 Watch out for these

The three mistakes students make most often with the quadratic formula.

1. Sign errors on −b

Wrong: for 2x² − 7x + 3 = 0, starting with −7. Right: b = −7, so −b = 7. Write b with its sign first.

2. Dividing only part of the numerator by 2a

Wrong: x = −b ± (√25)/2a. Right: the ENTIRE top (−b ± √25) is divided by 2a.

3. Forgetting to multiply by c in the discriminant

Wrong: for 3x² + 5x + 2 = 0, D = 25 − 4·3 = 13. Right: 4ac = 4·3·2 = 24, so D = 25 − 24 = 1.

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