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Question 220034
JEE Mathematics · Hard

Quadratic Equations and Inequalities: Transformed equation MCQ

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Transformed equationHardQuestion 220034

Question

If α and β are roots of x² − px + q = 0, an equation with roots α² and β² is:
  1. A
    x² − (p²−2q)x + q² = 0
    Correct
  2. B
    x² − (p²+2q)x + q² = 0
  3. C
    x² + (p²−2q)x + q² = 0
  4. D
    x² − p²x + q = 0

Correct answer

x² − (p²−2q)x + q² = 0

Explanation

New sum: α²+β² = (α+β)²−2αβ = p²−2q. New product: α²β² = (αβ)² = q². Equation: x²−(p²−2q)x+q²=0.

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