Three distinct positive real numbers a , b , c are in H.P. then for the quadratic equation x 2 − k x + 2 b 101 − a 101 − c 101 = 0 , k ∈ R has ((A) roots of same sign ((B) roots of opposite sign

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IF α , β ARE ROOTS THEN α β = 2 B 101 − A 101 − C 101 NOW 2 a 101 + c 101 ​ ≥ ( ac ​ ) 101 ≥ b 101 ⇒ 2 B 101 − A 101 − C 101 < 0 ⇒ α β < 0 ⇒ roots are opposite in sign.

Mathematics - Quadratic Equation Question with Solution | TestHub

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