Pure · Algebra & functions
Chapter 1 · 4
The idea
Quadratic equations
Three ways to solve a quadratic — factorising, completing the square, the formula — where the formula comes from, and what the discriminant tells you before you solve.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Pure · Algebra & functions
Quadratic equations
Three ways to solve a quadratic — factorising, completing the square, the formula — where the formula comes from, and what the discriminant tells you before you solve.
Why it works
Two, one or no solutions
A quadratic is with . Its graph is a parabola, so it can cross the -axis twice, touch it once, or miss it entirely — which is why a quadratic has two, one, or no real solutions.Factorising
Factorising rests on one fact: if two things multiply to , at least one of them is . So once you write , the solutions are simply or . The whole skill is finding and — two numbers that multiply to and add to (when ).Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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