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UP TGT Mathematics Algebra Test Series - Part 4

If α and β are roots of x^2 - px + q = 0, the quadratic equation whose roots are (α^2 / β) and (β^2 / α) is:

Type: MCQ • Marks: 1
If α and β are roots of x^2 - px + q = 0, the quadratic equation whose roots are (α^2 / β) and (β^2 / α) is:
Options
A. x^2 - p^2qx + q^3 = 0
B. qx^2 - (p^3 - 3pq)x + q^2 = 0
C. qx^2 + (p^3 - 3pq)x + q^2 = 0
D. qx^2 - p^3 x + q^2 = 0
Explanation
New sum = α^2/β + β^2/α = (α^3 + β^3)/αβ = [(p^3 - 3pq)] / q. New product = (α^2/β)(β^2/α) = αβ = q. Equation: x^2 - [(p^3 - 3pq)/q]x + q = 0 => qx^2 - (p^3 - 3pq)x + q^2 = 0.
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