Solving Quadratic Equations | 求解一元二次方程

📚 Solving Quadratic Equations | 求解一元二次方程

Quadratic equations appear in nearly every IGCSE Mathematics paper. Mastering the three main methods of solution — factorisation, completing the square, and the quadratic formula — is essential for success. This revision guide explains each method step by step, highlights common pitfalls, and provides exam-style advice.

一元二次方程几乎出现在每一份IGCSE数学试卷中。掌握三种主要的解法——因式分解法、配方法和求根公式——是取得高分的关键。本复习指南将逐步讲解每种方法，指出常见陷阱，并提供考试风格的建议。

1. What Is a Quadratic Equation? | 什么是一元二次方程？

A quadratic equation is a polynomial equation of degree 2, meaning the highest power of the variable is 2. The general form is:

一元二次方程是最高次数为2的多项式方程，即变量的最高次幂为2。其一般形式为：

ax² + bx + c = 0, 其中 a ≠ 0

Here a, b and c are constants, and x is the unknown. The coefficient a must not be zero, otherwise the equation would be linear, not quadratic.

其中 a、b、c 为常数，x 为未知数。系数 a 不能为零，否则方程将变为一次方程而非二次方程。

A solution of a quadratic equation is called a root. A quadratic equation always has exactly two roots in the set of complex numbers, but in IGCSE we usually work with real roots. The roots may be distinct, equal, or non-real.

二次方程的解称为根。在复数范围内，一元二次方程恰好有两个根；但在IGCSE中，我们通常研究实根。根可能是两个不同实根、两个相等实根，或没有实根。

2. Standard Form and the Quadratic Expression | 标准形式与二次多项式

Before solving, always rearrange the equation into the standard form ax² + bx + c = 0. For example, the equation 2x² + 5x = 3 must first become 2x² + 5x − 3 = 0 before applying any solution method.

Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

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