Solving Quadratic Equations by Factorisation | 因式分解法解二次方程

2026-08-21 18:59 · 本文部分内容由AI辅助创作

📚 Solving Quadratic Equations by Factorisation | 因式分解法解二次方程

A quadratic equation is one of the most important algebraic skills in IGCSE Mathematics. Factorisation is often the fastest method when the equation has rational roots, and it builds directly on your earlier work with brackets and linear equations.

二次方程是 IGCSE 数学中最重要的代数技能之一。当方程有有理数根时，因式分解法通常是最快的方法，它直接建立在括号展开和一次方程的基础上。

In the IGCSE exam, you may be asked to solve quadratic equations by factorisation, and you may also need to use the method as part of a larger problem. Mastering the technique will save you time and reduce careless errors.

在 IGCSE 考试中，你可能会被要求用因式分解法解二次方程，也可能需要在更大的问题中用到这个方法。掌握这项技巧可以节省时间并减少粗心错误。

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

and a ≠ 0. The condition a ≠ 0 is essential because if a = 0 the equation becomes linear.

二次方程是次数为 2 的多项式方程，即变量 x 的最高次数是 2。在 IGCSE 中，你会看到它写成标准形式 ax² + bx + c = 0，其中 a、b、c 是常数且 a ≠ 0。条件 a ≠ 0 很重要，因为如果 a = 0，方程就变成了一次方程。

Examples include x² + 5x + 6 = 0, 2x² − 3x + 1 = 0 and 4x² − 9 = 0.

例如 x² + 5x + 6 = 0、2x² − 3x + 1 = 0 和 4x² − 9 = 0。

t, such as x(x + 3) = 4, but after expanding and rearranging they take the quadratic form.

有些方程一开始看起来不像二次方程，例如 x(x + 3) = 4，但展开并整理后会变成二次形式。

2. Standard Form and Terminology | 标准形式与术语

Before solving, you should always rearrange the equation so that one side is zero and the powers of x are in descending order. This helps you identify the quadratic term, the linear term and the constant term.

在求解之前，你应先把方程整理为一边等于零、且 x 的幂按降序排列。这有助于你识别二次项、一次项和常数项。