Solving Quadratic Equations | 解二次方程

📚 Solving Quadratic Equations | 解二次方程

Quadratic equations appear throughout the IGCSE Mathematics syllabus. Mastering them is essential for both Paper 1 and Paper 2. In this revision guide, you will learn the most efficient methods, see worked examples, and avoid common mistakes.

二次方程贯穿 IGCSE 数学全部大纲。掌握二次方程对 Paper 1 和 Paper 2 都至关重要。在本复习指南中，你将学到最高效的方法、典型例题以及常见错误规避。

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

A quadratic equation is an equation of the form ax² + bx + c = 0, where a ≠ 0. The highest power of x is 2. If a = 0, the equation becomes linear.

二次方程是形如 ax² + bx + c = 0 的方程，其中 a ≠ 0。未知数 x 的最高次数为 2。如果 a = 0，方程就退化为一次方程。

Here are some examples and non-examples:

下面是一些是二次方程与不是二次方程的例子：

• 2x² + 3x − 5 = 0 is a quadratic equation (a=2, b=3, c=−5).

  2x² + 3x − 5 = 0 是二次方程（a=2，b=3，c=−5）。

• x² − 4 = 0 is quadratic, because b can be 0.

  x² − 4 = 0 也是二次方程，因为 b 可以为 0。

• x + 3 = 0 is not quadratic, as the x² term is missing.

  x + 3 = 0 不是二次方程，因为缺少 x² 项。

In the form ax² + bx + c = 0, the constants a, b and c are usually integers, and x is the unknown.

在 ax² + bx + c = 0 中，通常 a、b、c 为常数，x 为未知数。

2. Solving by Factorisation | 因式分解法

The simplest way to solve a quadratic is to write it as a product of two brackets and then use the zero-product property: if AB = 0, then A = 0 or B = 0.

最简单的解法是把二次式写成两个括号相乘，然后利用零积性质：如果 AB = 0，则 A = 0 或 B

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