Quadratic Equations: Factorising, Completing the Square and the Quadratic Formula | 二次方程：因式分解、配方法与求根公式

📚 Quadratic Equations: Factorising, Completing the Square and the Quadratic Formula | 二次方程：因式分解、配方法与求根公式

Quadratic equations appear throughout the IGCSE Mathematics syllabus, from algebra and problem solving to graphs and real-world modelling. A quadratic equation is any equation that can be written in the standard form ax² + bx + c = 0, where a ≠ 0. This article explains four essential methods: factorising, completing the square, using the quadratic formula, and interpreting the discriminant.

二次方程贯穿 IGCSE 数学大纲，从代数、问题求解到图像和现实建模都会出现。二次方程是任何可以写成标准形式 ax² + bx + c = 0 的方程，其中 a ≠ 0。本文讲解四种核心方法：因式分解、配方法、使用求根公式以及判别式的解读。

1. Recognising a Quadratic Equation | 识别二次方程

A quadratic equation has the highest power of x equal to 2. The standard form is ax² + bx + c = 0, where a, b and c are constants and a cannot be zero. If a were zero, the equation would become linear.

二次方程中 x 的最高次数是 2。标准形式为 ax² + bx + c = 0，其中 a、b、c 是常数，且 a 不能为零。如果 a 为零，方程就变成了一次方程。

For example, 2x² + 5x – 3 = 0 is quadratic, while 3x + 1 = 0 is linear. In IGCSE questions, the quadratic may not be given in standard form; you must expand brackets or collect like terms first.

例如，2x² + 5x – 3 = 0 是二次方程，而 3x + 1 = 0 是一次

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