If α and β are the roots of the equation

If α and β are the roots of the equation x² - 11x + 24 = 0, find the equation having the roots α + 2 and β + 2

1. x² + 15x + 24 = 0
2. x² - 15x + 24 = 0
3. x² + 15x - 50 = 0
4. x² + 15x - 60 = 0
5. x² - 15x + 50 = 0

Given equation is
x² - 11x + 24 = 0
Then, required equation is
(x - 2)² - 11(x - 2) + 24 = 0
⇒ x² - 4x + 4 - 11x + 22 + 24 = 0
⇒ x² - 15x + 50 = 0