Quadratic Equations: Complete IGCSE Revision | 二次方程：IGCSE 完整复习指南

📚 Quadratic Equations: Complete IGCSE Revision | 二次方程：IGCSE 完整复习指南

A quadratic equation is one of the most important topics in IGCSE Mathematics. It appears in almost every paper, either directly as an algebra question or indirectly within geometry, sequences, and problem-solving contexts. Understanding how to solve quadratics fluently is essential for achieving a high grade.

二次方程是 IGCSE 数学中最重要的话题之一。它几乎出现在每份试卷中，要么直接作为代数题出现，要么间接出现在几何、数列和实际应用题中。熟练掌握解二次方程的方法对于取得高分至关重要。

1. What Is a Quadratic Equation? | 什么是二次方程？

A quadratic equation is an equation in which the highest power of the unknown variable is 2. The general form is written as ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. If a = 0, the equation becomes linear, not quadratic.

二次方程是未知数最高次数为 2 的方程。其一般形式写作 ax² + bx + c = 0，其中 a、b、c 为常数，且 a ≠ 0。如果 a = 0，方程就变成了一次方程（线性方程），而不是二次方程。

The word ‘quadratic’ comes from the Latin ‘quadratus’, meaning ‘square’. This is because the variable is squared. For example, x² + 5x + 6 = 0 is a quadratic equation, while 2x + 3 = 0 is not.

“二次”（quadratic）一词源自拉丁语“quadratus”，意为“正方形”。这是因为方程中的变量被平方了。例如，x² + 5x + 6 = 0 是一个二次方程，而 2x + 3 = 0 则不是。

2. The Standard Form | 标准形式

Before solving any quadratic equation, it is often helpful to rearrange it into standard form:

在解任何二次

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