Solving Quadratic Equations | 解二次方程

📚 Solving Quadratic Equations | 解二次方程

Quadratic equations are one of the most frequently examined topics in IGCSE Mathematics. Whether you are solving them directly, using them in word problems, or sketching their graphs, a solid grasp of quadratics will unlock marks across many areas of the syllabus. This guide walks through every essential method step by step.

二次方程是 IGCSE 数学考试中出现频率最高的考点之一。无论是直接求解、应用于文字应用题，还是绘制二次函数图像，熟练掌握二次方程都能帮助你在考纲的多个板块获得分数。本指南将逐步讲解每一个核心方法。

1. The Standard Form of a Quadratic Equation | 二次方程的标准形式

A quadratic equation is any equation that can be written in the standard form ax² + bx + c = 0, where a, b and c are constants, and a ≠ 0. The coefficient a must not be zero because if a = 0, the equation reduces to a linear equation bx + c = 0.

二次方程是指可以写成标准形式 ax² + bx + c = 0 的方程，其中 a、b、c 为常数，且 a ≠ 0。系数 a 不能为零，因为如果 a = 0，方程就退化为线性方程 bx + c = 0。

Each part of the standard form has a specific role: a is the coefficient of x², b is the coefficient of x, and c is the constant term. For example, in 2x² – 3x + 7 = 0, we have a = 2, b = -3 and c = 7.

标准形式中的每一部分都有特定作用：a 是 x² 的系数，b 是 x 的系数，c 是常数项。例如，在 2x² – 3x + 7 = 0 中，a = 2，b = -3，c = 7。

Notice that a quadratic equation must contain an x² term, but

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