Question Detail
Question
Find the equation whose roots are the squares of the roots of \( x^2 + x + 2 = 0 \).
Correct Answer
Option A is the correct answer.
Detailed Explanation
Let α and β be the roots of x² + x + 2 = 0. Then α+β = -1, αβ = 2. We want the equation with roots α² and β². Sum = α²+β² = (α+β)² - 2αβ = (-1)² - 2(2) = 1 - 4 = -3. Product = α²β² = (αβ)² = 2² = 4. The quadratic with these roots is x² - (sum)x + product = 0 => x² - (-3)x + 4 = 0 => x² + 3x + 4 = 0.
Hint
Use the transformation of roots: find the sum and product of the new roots in terms of the original sum and product.