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Problem 1 - Olympiad

If α and β are roots of x² - 5x + 6 = 0, find the equation whose roots are α + 2 and β + 2

Correct: B

Given α + β = 5 and αβ = 6. New roots: α + 2 and β + 2. Sum = (α + 2) + (β + 2) = α + β + 4 = 5 + 4 = 9. Product = (α + 2)(β + 2) = αβ + 2α + 2β + 4 = 6 + 4 + 10 = 20. The equation becomes x² - (sum)x + product = 0 ⇒ x² - 9x + 20 = 0.