How to quickly solve quadratic equations in CAT?

RAHUL SINGH
Apr 10
2 min read

Quadratic equations are a crucial part of the Quantitative Aptitude section in CAT. These equations appear frequently and can be solved efficiently using smart techniques. In this blog, we will discuss the best strategies to solve quadratic equations quickly and accurately, helping you save valuable time during the exam.

Understanding Quadratic Equations

A quadratic equation is a polynomial equation of the form:

ax² + bx + c = 0

where a, b, and c are constants, and x is the variable.

Quick Techniques to Solve Quadratic Equations

1. Factorization Method (Preferred for Simplicity)

Find two numbers that multiply to ac and add up to b.
Split the middle term accordingly.
Factorize and solve for x.
Example:
- x² + 7x + 10 = 0 → (x + 5)(x + 2) = 0 → x = -5 or x = -2

2. Quadratic Formula (For Complex Equations)

Use the formula:

x = (-b ± √(b² - 4ac)) / 2a

This is helpful when factorization is not straightforward.

3. Completing the Square

Convert the equation into the form (x + p)² = q.
Solve for x by taking the square root.
Example:
- x² + 6x + 9 = 0 → (x + 3)² = 0 → x = -3

4. Shortcut for Finding Roots

For a quadratic equation x² + (sum of roots)x + (product of roots) = 0, use:

Sum of roots = -b/a
Product of roots = c/a. This helps in quickly identifying the roots without detailed calculations.

5. Special Cases to Save Time

If the discriminant (b² - 4ac) is a perfect square, factorization is easy.
For equations in the form x² - k² = 0, use (x - k)(x + k) = 0 directly.

Common Mistakes to Avoid

Forgetting to check for imaginary roots (when b² - 4ac < 0).
Missing negative signs while using the quadratic formula.
Rushing through factorization without verifying the multiplication.

Practice Makes Perfect

Solve previous years' CAT questions on quadratic equations.
Take mock tests at Rahul Sir's Classes to improve speed and accuracy.
Time yourself while solving quadratic equations to build efficiency.

Conclusion

Mastering quadratic equations can significantly boost your CAT score. By using quick methods like factorization, the quadratic formula, and completing the square, you can solve these problems in seconds. Keep practicing and refining your approach to ensure accuracy and speed.

Looking for expert guidance? Join Rahul Sir's Classes today and get personalized coaching, mock tests, and strategic preparation tips to crack CAT with ease!