Mastering Quadratic Equations for IGCSE Mathematics | 掌握 IGCSE 数学二次方程

📚 Mastering Quadratic Equations for IGCSE Mathematics | 掌握 IGCSE 数学二次方程

Quadratic equations are one of the most important algebraic skills in IGCSE Mathematics. They appear in algebra, graphs, problem solving, and even trigonometry or physics-style questions. A quadratic equation is any equation in which the highest power of the unknown is 2, such as x² + 3x – 4 = 0. In this article you will learn how to recognise, solve, sketch, and check quadratic equations using three main methods: factorising, completing the square, and the quadratic formula.

二次方程是 IGCSE 数学中最重要的代数技能之一。它们出现在代数、图像、解决问题甚至三角学或物理类题目中。二次方程是指未知数的最高次数为 2 的方程，例如 x² + 3x – 4 = 0。本文将教你如何识别、求解、画出并检验二次方程，包括三种主要方法：因式分解法、配方法和求根公式法。

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

A quadratic equation is a polynomial equation of degree 2. This means the highest power of the variable, usually x, is 2. In IGCSE Mathematics, the standard disguise is x² + bx + c = 0, but the coefficient of x² may also be different from 1. For example, 2x² – 5x + 3 = 0 and x² – 9 = 0 are both quadratic equations. A linear equation such as 3x + 1 = 0 is not quadratic because its highest power of x is 1. The word quadratic comes from the Latin quadratus, meaning square.

二次方程是次数为 2 的多项式方程。这意味着变量（通常是 x）的最高次幂为 2。在 IGCSE 数学中，常见形式为 x² + bx + c = 0，但 x² 的系数也可以不等于 1。例如 2x² – 5x + 3 = 0 和 x² – 9 = 0 都是二次方程。线性方程如 3x + 1 = 0 不是二次方程，因为 x 的最高次幂是 1。quadratic 一词来自拉丁语 quadratus，意思是正方形。

Recognising a quadratic is important before you start solving

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