IGCSE Maths: Solving Quadratic Equations | IGCSE 数学：二次方程求解

📚 IGCSE Maths: Solving Quadratic Equations | IGCSE 数学：二次方程求解

Quadratic equations are central to IGCSE Mathematics. They appear in algebra, coordinate geometry, and real-world problems such as area, projectile motion, and number patterns. This guide covers the three main solving methods: factorisation, completing the square, and the quadratic formula. You will also learn how to use the discriminant and how to link equations to their graphs.

二次方程是 IGCSE 数学的核心内容。它们出现在代数、坐标几何和现实问题中，例如面积、抛体运动和数字规律。本指南涵盖三种主要求解方法：因式分解法、配方法和求根公式法。你还将学习如何使用判别式，以及如何将方程与图像联系起来。

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 variable is 2. The standard form is ax² + bx + c = 0, where a, b and c are constants and a ≠ 0.

二次方程是变量的最高次数为 2 的方程。其标准形式为 ax² + bx + c = 0，其中 a、b 和 c 为常数，且 a ≠ 0。

If a = 0, the x² term disappears and the equation becomes linear. The condition a ≠ 0 is therefore essential. In IGCSE, quadratic equations usually have two real solutions, one repeated real solution, or no real solutions.

如果 a = 0，x² 项消失，方程就变成一次方程。因此条件 a ≠ 0 至关重要。在 IGCSE 中，二次方程通常有两个实数解、一个重复实数解或没有实数解。

For example, x² – 9 = 0 is quadratic because the highest power of x is 2. It can be solved quickly as x² = 9, giving x = ±3.

例如，x² – 9 = 0 是二次方程，因为 x 的最高次数为 2。它可以快速求解：x² = 9，得 x = ±3。

2. Standard Form and Coefficients | 标准形式与系数

Before solving, always rearrange the equation into standard form ax² + bx + c = 0. Then identify the coefficients a, b and

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