Quadratic formula practice

Practice session

What you practise

First work out D = b² − 4ac, then both roots with ±. Type two roots as 2; 3 or as 2 or 3. To see what D means on a graph, open the parabola simulation.

Example

Calculate the solutions of x² − 5x + 6 = 0.

1. D = 25 − 24 = 1
2. x = (5 ± 1) / 2
3. x = 3 or x = 2

Answer: 2; 3.

What you need to know

The quadratic formula in the 2027 central exam syllabus (wiskunde B). Only levels with a source are listed, and it is not a full exam list.

havo · wiskunde B · domain B (B2)

Functies, grafieken en vergelijkingen, part “kwadratische vergelijkingen” (quadratic equations) · source syllabus wiskunde B havo 2027 (Examenblad)

• Discriminant D = b² − 4ac
• Both roots with the quadratic formula (±)
• Keeping the sign of b right

vwo · wiskunde B · domain B (B5)

Functies, grafieken en vergelijkingen, part “kwadratische vergelijkingen” (quadratic equations) · source syllabus wiskunde B vwo 2027 (Examenblad)

• What D > 0, D = 0 and D < 0 mean
• Two real roots or no real solutions

Formula sheet

Print-friendly: use Print in your browser.

• Discriminant $$D=b^2-4ac$$
• Quadratic formula $$x=\frac{-b\pm \sqrt{D}}{2a}$$
• Example x² − 5x + 6 = 0 → x = 2 or x = 3 $$x=\frac{5\pm 1}{2}$$

Discriminant

D = b² − 4ac. It tells you whether there are real roots (D ≥ 0) or none (D < 0).

abc-formule

The Dutch name for the quadratic formula x = (−b ± √D) / (2a), for ax² + bx + c = 0 with a ≠ 0.

Practice with real exam questions on Examenblad.nl (in Dutch). We do not host past exams.

Frequently asked questions

What if D < 0?

Then there are no real solutions. Most questions in this set have D ≥ 0.

Which calculator goes with this?

The quadratic formula calculator.