Question

If α and β are roots of equation x² - 15x + 56 = 0 then find the value of (α² – β²) where α > β?
1. 15
2. 12
3. 18
4. 20

Answer 1

Correct Answer - Option 1 : 15

Given:

The given quadratic equation = x² - 15x + 56

Calculation:

x² - 15x + 56 = 0

⇒ x² - 8x – 7x + 56 = 0

⇒ x(x - 8) - 7(x - 8) = 0

⇒ (x - 8)(x - 7) = 0

⇒ x = 7 and 8

So, α and β are 8 and 7 respectively.

∴ (α² – β²) = (8)² – (7)² = 15