Question

If positive numbers a^–1, b^–1, c^–1 are in A.P. then product of

roots of equation x² – kx + 2b¹⁰¹ – a¹⁰¹– c¹⁰¹ = 0 (k Ī R) has

• A.
  • ve sign
• B. – ve sign
• C. 0
• D. None

Answer 1

Answer: (B)

– ve sign

Answer 2

a,b,c Ž in H.P.

$\frac{a^{101} + c^{101}}{2}$ > $(\sqrt{ac})^{101}$ > b¹⁰¹

Ž 2b¹⁰¹ – a¹⁰¹ – c¹⁰¹ < 0

Ž product < 0