📚 Mastering Quadratic Equations | 掌握二次方程
Quadratic equations are one of the most important topics in IGCSE Mathematics. They appear in almost every paper, either as direct questions or as part of coordinate geometry, graph sketching, and word problems. Understanding how to solve them confidently can significantly boost your exam score.
二次方程是IGCSE数学中最重要的知识点之一。几乎每张试卷都会出现二次方程，无论是直接考查，还是作为坐标几何、函数图像和应用题的一部分。熟练掌握二次方程的解法，能显著提高你的考试成绩。
1. What Is a Quadratic Equation | 什么是二次方程
are constants and a ≠ 0. The highest power of the variable x is 2, which is why it is called "quadratic".
二次方程是形如 ax² + bx + c = 0 的方程，其中 a、b、c 为常数，且 a ≠ 0。变量 x 的最高次数为 2，因此称为"二次"方程。
a quadratic equation with a = 2, b = -5, and c = 3. If a = 0, the equation becomes linear.
例如，2x² - 5x + 3 = 0 就是一个二次方程，其中 a = 2，b = -5，c = 3。如果 a = 0，方程就退化为一元一次方程。
ax² + bx + c = 0, a ≠ 0
A quadratic equation can have at most two real solutions, also called roots. These roots may be distinct, equal, or non-real (complex), depending on the value of the discriminant.
二次方程最多有两个实数解，也称为根。根据判别式的值，这两个根可能不相等、相等或无实数解（复数解）。
2. Solving by Factorization | 因式分解法
Factorization is the simplest method when the quadratic expression can be quickly factored. The idea is to rewrite ax² + bx + c as the product of two linear factors, then set each factor to zero.
当二次表达式能够快速分解时，因式分解法是最简捷的方法。其核心思想是将 ax² + bx + c 改写成两个一次因式的乘积，然后令每个因式等于零。
Example | 例： Solve x² - 5x + 6 = 0. 解方程 x² - 5x + 6 = 0。
Step 1 | 第一步： Find two numbers that multiply to 6 and add to -5. These are -2 and -3.
找到两个数，乘积为 6，和为 -5。这两个数是 -2 和 -3。
Step 2 | 第二步： Write the factored form:
写出因式分解形式：
(x - 2)(x - 3) = 0
Step 3 | 第三步： Set each factor to zero:
令每个因式为零：
x - 2 = 0 ⇒ x = 2, or x - 3 = 0 ⇒
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