Solving Quadratic Equations

A quadratic equation contains a term in x² and can be written in the form ax² + bx + c = 0. This lesson covers solving by factorising, the quadratic formula, and completing the square (Higher), along with interpreting solutions in context.

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Key Vocabulary

Term	Meaning
Quadratic equation	An equation of the form ax² + bx + c = 0
Root / solution	A value of x that satisfies the equation
Discriminant	b² − 4ac — determines the number of solutions
Completing the square	Writing ax² + bx + c in the form a(x + p)² + q

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Solving by Factorising

If a product of factors equals zero, at least one factor must be zero.

Method

1. Rearrange so one side equals 0.
2. Factorise.
3. Set each factor equal to 0 and solve.

Worked Example 1

Solve: x² + 5x + 6 = 0

Step 1: Factorise: (x + 2)(x + 3) = 0