Question

If \( \alpha, \beta \) are the roots of \( x^2 - 3x + 1 = 0 \), then the equation whose roots are \( \frac{1}{\alpha - 2} \) and \( \frac{1}{\beta - 2} \) is:

• A. \( x^2 + y^2 + 4x - 10y + 25 = 0 \)
• B. \( x^2 - x - 1 = 0 \)
• C. \( x^2 + x - 1 = 0 \)
• D. None of these

Hint:

For quadratic equations with roots, use Vieta's formulas to find the sum and product of the roots, and then apply the transformations as needed.

Answer 1

The Correct Option is B