0Introduction
Quadratic equations are one of the most important topics in engineering entrance exams such as JEE and CET. Many students find it time-consuming to solve these questions, especially under exam pressure. In this lesson, we will understand a simple and effective method to solve quadratic equations quickly and accurately.
Concept Overview
A quadratic equation is generally written as:
ax² + bx + c = 0, where a ≠ 0
The roots of the equation can be found using the quadratic formula. However, in many cases, faster methods such as factorization can be applied to save time.
Shortcut Method (Factorization)
Instead of directly using the formula, try to split the middle term.
Example:
Solve: x² + 5x + 6 = 0
Step 1: Find two numbers whose sum is 5 and product is 6
Numbers are 2 and 3
Step 2: Rewrite the equation
x² + 2x + 3x + 6 = 0
Step 3: Factorize
x(x + 2) + 3(x + 2) = 0
Step 4: Final Answer
(x + 2)(x + 3) = 0
So, x = -2, -3
When to Use This Method
- When coefficients are simple
- When numbers are easily factorable
- Useful in MCQs for saving time
Conclusion
Practicing factorization techniques can significantly improve speed and accuracy in exams. Students should first check if factorization is possible before applying longer methods.
