Bank Exam Speed Maths

Page 17: Quadratic Equations (Shortcut Methods)

1. Basic Concept

Quadratic Equation: ax² + bx + c = 0

Roots Formula:
x = [-b ± √(b² - 4ac)] / 2a

2. Factorization Method (Fastest)

Convert equation into factors:

Example:
x² - 5x + 6 = 0
(x - 2)(x - 3) = 0
Roots = 2, 3

3. Root Comparison Trick

Solve both equations separately and compare roots

Example:
x² - 7x + 10 = 0 → roots = 2, 5
x² - 5x + 6 = 0 → roots = 2, 3
Compare → one root equal (2)

4. Nature of Roots

D = b² - 4ac

D > 0 → Real & different
D = 0 → Equal roots
D < 0 → Imaginary roots

5. Shortcut Method

Sum of roots = -b/a
Product of roots = c/a

Example:
x² - 5x + 6 = 0
Sum = 5, Product = 6 → Roots = 2, 3

6. Important Tips

• Prefer factorization over formula

• Use sum & product for quick solving

• Common in comparison questions

7. Practice Questions

1. Solve: x² - 9x + 20 = 0

2. Roots of x² - 4x + 4 = 0?

3. Compare roots: x² - 6x + 8 and x² - 5x + 6

4. Find sum of roots of x² - 7x + 10

5. Nature of roots: x² + 4x + 5