📚 Mastering Quadratic Equations for IGCSE Mathematics | 掌握IGCSE数学二次方程
Quadratic equations appear throughout the IGCSE Mathematics syllabus, from pure algebra and coordinate geometry to real-life modelling. A strong understanding of their standard form, solution methods and graphs will help you tackle both structured questions and word problems with confidence.
二次方程贯穿IGCSE数学课程，从纯代数和坐标几何到实际建模都会出现。深入理解二次方程的标准式、求解方法和图像，将帮助你自信地应对结构化题目和应用题。
1. Standard Form and Key Terms | 标准式与关键术语
ants and a ≠ 0. The term ax² is the quadratic term, bx is the linear term, and c is the constant term.
一元二次方程是指可以写成 ax² + bx + c = 0 的方程，其中 a、b、c 为常数且 a ≠ 0。ax² 称为二次项，bx 称为一次项，c 称为常数项。
0, the equation becomes linear, so the condition a ≠ 0 is essential for a true quadratic.
例如，在 2x² − 5x + 3 = 0 中，a = 2，b = −5，c = 3。如果 a = 0，方程就变成一次方程，因此 a ≠ 0 这一条件是二次方程成立的关键。
dard form before identifying a, b and c. For example, x² = 4x − 7 becomes x² − 4x + 7 = 0.
在确定 a、b、c 之前，务必先将方程整理为标准式。例如，x² = 4x − 7 应改写为 x² − 4x + 7 = 0。
2. Solving by Factorising | 因式分解法
Factorising works best when the quadratic expression can be written as a product of two linear brackets. Look for two numbers that multiply to give ac and add to give b, then split the middle term or write the brackets directly.
当二次式可以写成两个一次因式的乘积时，因式分解法最为有效。寻找两个数，使它们的乘积为 ac，和为 b，然后拆分中项或直接写成括号形式。
roduct 12 and sum −7; they are −3 and −4. Therefore (x − 3)(x − 4) = 0, so x = 3 or x = 4.
例如：x² − 7x + 12 = 0。我们需要乘积为 12、和为 −7 的两个数，即 −3 和 −4。因此 (x − 3)(x − 4) = 0，所以 x = 3 或 x = 4。
For a quadratic with a leading coefficient not equal to 1, such as 2x² + 5x − 3, find two numbers that multiply to −6 and add to 5: these
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