Cambridge IGCSE Mathematics 0580 · 2027 · Extended

Quadratics: three methods

A free topic pilot, not a complete IGCSE course. No account or payment needed.

Extended Paper 2 is non-calculator; Paper 4 requires a scientific calculator. Questions here are non-calculator practice except Q08, which is marked calculator practice. The quadratic formula is supplied in the official Extended formula list.

Start with the method you need

A compact introduction to three quadratic-solving methods. Not a complete syllabus course or exam-grade predictor. There are three questions per step and three in the final check. Write your working before selecting an answer.

Factorise and solve

Start with one side equal to zero.

Factorise fully, then set each variable factor equal to zero.

Check every root in the original equation; never divide by x when x might be zero.

Complete the square

For x² + bx + c, half b inside the square and correct the constant outside.

For ax² + bx + c, first factor a out of the x² and x terms.

When solving (x + p)² = q with q positive, use both square-root signs. Keep exact surds when requested.

Use the quadratic formula

First write ax² + bx + c = 0 and identify signed a, b and c.

Use x = (−b ± √(b² − 4ac))/(2a), with brackets around the entire numerator.

Use both signs, simplify exact answers, or round only at the end to the requested accuracy.

Try factorising now · Try the three-question final check

Try all three without hints, then review the worked solutions. This short check is practice, not a validated grade prediction.