Solving Quadratic Equations: Factorising, Completing the Square and the Formula | IGCSE数学：解二次方程——因式分解、配方法与公式法

📚 Solving Quadratic Equations: Factorising, Completing the Square and the Formula | IGCSE数学：解二次方程——因式分解、配方法与公式法

Quadratic equations appear throughout the IGCSE Mathematics syllabus, from pure algebra to geometry, measurement and word problems. This article brings together the three main algebraic methods – factorising, completing the square and the quadratic formula – and shows how each method connects to the graph of a parabola.

二次方程贯穿 IGCSE 数学大纲，从纯代数到几何、测量和应用题都会用到。本文汇总三种主要代数方法——因式分解、配方法和二次公式法，并说明每种方法与抛物线图像之间的联系。

1. Recognising Quadratic Equations | 识别二次方程

A quadratic equation is an equation that can be written in the form ax² + bx + c = 0, where a ≠ 0. The highest power of the unknown x is 2, which is why it is called ‘quadratic’ or second-degree.

二次方程是可写成 ax² + bx + c = 0 形式的方程，其中 a ≠ 0。未知数 x 的最高次数为 2，因此称为二次方程或二阶方程。

For example, x² – 5x + 6 = 0 and 2x² + 3x – 4 = 0 are quadratic equations, but x³ + x² = 0 is not.

例如 x² – 5x + 6 = 0 和 2x² + 3x – 4 = 0 是二次方程，而 x³ + x² = 0 不是。

2. Standard Form and Core Terms | 标准形式与核心术语

The standard form is ax² + bx + c = 0. Here a, b and c are real numbers, and a cannot be zero. The term ax² is called the quadratic term, bx is the linear term, and c is the constant term.

标准形式为 ax² + bx + c = 0。其中 a、b、c 为实数，且 a 不能为零。ax² 称为二次项，bx 称为一次项，c 称为常数项。

Before solving, always rearrange the equation into standard form

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