IGCSE Maths Topic 2: Quadratic Equations (T-2-1055) | IGCSE 数学专题 2：二次方程（T-2-1055）

📚 IGCSE Maths Topic 2: Quadratic Equations (T-2-1055) | IGCSE 数学专题 2：二次方程（T-2-1055）

Quadratic equations are one of the most tested algebra topics in IGCSE Mathematics. This revision guide covers solving methods, the discriminant, graphing, inequalities and real-life applications, with clear bilingual explanations and worked examples for exam success.

二次方程是 IGCSE 数学中最常考的代数主题之一。本复习指南涵盖求解方法、判别式、图像、不等式和实际应用，并提供清晰的中英双语讲解和例题，帮助你在考试中取得成功。

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

A quadratic equation is any equation that can be written in the standard form ax² + bx + c = 0, where a, b and c are constants and a ≠ 0. The highest power of the variable x is 2, so the graph is always a parabola.

二次方程是任何可以写成标准形式 ax² + bx + c = 0 的方程，其中 a、b、c 为常数且 a ≠ 0。变量 x 的最高次数是 2，因此它的图像总是一条抛物线。

For example, x² + 5x + 6 = 0, 2x² − 3x − 2 = 0 and x² − 9 = 0 are all quadratic equations. The equation x³ + 2x − 1 = 0 is not quadratic because the highest power is 3.

例如，x² + 5x + 6 = 0、2x² − 3x − 2 = 0 和 x² − 9 = 0 都是二次方程。方程 x³ + 2x − 1 = 0 不是二次方程，因为最高次数是 3。

Quadratic equations appear in many IGCSE questions, from simple factorisation to word problems involving area or projectile motion. Recognising the standard form immediately will save time in the exam.

二次方程出现在许多 IGCSE 考题中，从简单的因式分解到涉及面积或抛体运动的文字题。能够立即识别标准形式将帮助你在考试中节省时间。

2. Standard Form and Key Terms | 标准形式与关键术语

In the standard form ax² + bx + c = 0, a is called the leading coefficient, b is the linear coefficient, and c is the constant term. a cannot be zero, otherwise the equation becomes linear.

在标准形式 ax² + bx + c = 0 中，a 称为二次项系数，b 称为一次项系数，c 称为常数项。a 不能为零，否则方程就变成一次方程。

Solutions of a quadratic equation are called roots, zeros or x-intercepts. A root is a value of x that makes the equation true. A quadratic equation can have two real roots, one repeated real root, or no real roots depending on the discriminant.

二次方程的解称为根、零点或 x 轴截距。根是使方程成立的 x 值。根据判别式的不同，二次方程可能有两个实根、一个重根或没有实根。

For example, the equation x² + x − 2 = 0 has roots x = 1 and x = −2 because substituting either value gives zero. These roots are also the points where the graph crosses the x-axis.

例如，方程 x² + x − 2 = 0 的根为 x = 1 和 x = −2，因为代入任一值都使方程等于零。这些根同时也是图像与 x 轴的交点。

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