How to Solve IGCSE Quadratic Equations Step by Step

Master the three main methods for solving quadratic equations in IGCSE Maths: factorising, completing the square, and the quadratic formula with worked examples.

Factorising Quadratic Equations

Factorising is the fastest method for solving quadratics when it works, and IGCSE examiners expect you to try it first. The key is to find two numbers that multiply to give the constant term (c) and add to give the coefficient of x (b). For example, x² + 5x + 6 = 0 factors to (x + 2)(x + 3) = 0, giving solutions x = -2 and x = -3. When the leading coefficient is not 1, use the grouping method: multiply a by c, find two numbers with that product and sum b, then split the middle term and factor by grouping.

Completing the Square and the Quadratic Formula

Completing the square rewrites ax² + bx + c into the form a(x + p)² + q, which reveals the vertex of the parabola and solves equations that do not factorise neatly. Halve the coefficient of x, square it, then add and subtract that value inside the expression. The quadratic formula x = (-b ± sqrt(b² - 4ac)) / 2a works for every quadratic and is given on the IGCSE formula sheet, so memorising it is not necessary — but practising its use is essential. Pay close attention to the discriminant b² - 4ac: if positive you get two real solutions, if zero one repeated root, and if negative no real solutions.

Choosing the Right Method in Exams

In IGCSE exams, the question wording tells you which method to use. If it says "factorise", you must show the bracket form — using the formula will score zero even if the answer is correct. If it says "give your answer to 2 decimal places", factorising will not work and you should use the quadratic formula. For "complete the square" questions, show every step of the rearrangement. When no method is specified, try factorising first because it is fastest; if the numbers do not work within 30 seconds, switch to the formula immediately to save time.

Quadratic equations appear in almost every IGCSE Maths paper. Mastering all three methods — and knowing when to use each — is one of the most efficient ways to secure marks. If you need targeted practice, book a free session to work through exam-style questions together.