Solving Quadratic Equations | 解二次方程

📚 Solving Quadratic Equations | 解二次方程

Quadratic equations are one of the most fundamental topics in IGCSE Mathematics. You will meet them in algebra, graphs, coordinate geometry, and word problems. This article explains the main methods of solving quadratic equations, including factorisation, the quadratic formula, and completing the square, with clear examples and exam tips.

二次方程是 IGCSE 数学中最基础的主题之一。你将在代数、图像、坐标几何和应用题中遇到它们。本文讲解解二次方程的主要方法，包括因式分解法、求根公式法和配方法，并配有清晰的例题和考试提示。

1. Recognising Quadratic Equations | 识别二次方程

Not every equation containing x² is quadratic. The defining feature is that the highest power of the variable is exactly 2, with no higher powers present. For example, x² = 4, 2x² + 3x = 1 and (x – 1)(x + 2) = 0 can all be rearranged into the standard form. However, x³ + x² = 0 is cubic, not quadratic.

并非所有含有 x² 的方程都是二次方程。二次方程的核心特征是变量的最高指数恰好为 2，且没有更高次幂。例如 x² = 4、2x² + 3x = 1 和 (x – 1)(x + 2) = 0 都可以化为标准形式。但 x³ + x² = 0 是三次方程，不是二次方程。

2. Standard Form and Simplification | 标准形式与化简

Always rearrange the equation into ax² + bx + c = 0 before solving. Remove brackets, combine like terms, and bring all nonzero terms to one side. For example, 2x² + 3x = 1 becomes 2x² + 3x – 1 = 0. This step is essential because all solution methods assume the right-hand side is zero.

求解前务必将方程重写为 ax² + bx + c = 0 的形式。去括号、合并同类项，并将所有非零项移到一侧。例如，2x² + 3x = 1 可化为 2x² + 3x – 1 =

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