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 roots be α, β. Then α+β = -1, αβ=2. New roots: α², β². Sum = α²+β² = (α+β)² - 2αβ = 1 - 4 = -3. Product = (αβ)² = 4. Equation: x² - (sum)x + product = 0 ⇒ x² - (-3)x + 4 = 0 ⇒ x² + 3x + 4 = 0.
Hint
Use α²+β² = (α+β)² - 2αβ and α²β² = (αβ)².