DeterminantHard
Question
The determinent ᐃ = 
is equal to zero if
is equal to zero ifOptions
A.b, c, d are in A.P.
B.b, c, d are in G.P.
C.b, c, d are in H.P.
D.α is a root of ax3 - bx2 - 3cx - d = 0
Solution
ᐃ = 
Applying C3 → C3 - (C1a + C2)
ᐃ =
= 0
(aα3 - bα2 - 3cα - d) (bd - c2) = 0
∴ Either b, c, d in G.P. or α is root of ax3 - bx2 - 3cx - d = 0
Applying C3 → C3 - (C1a + C2)
ᐃ =
= 0 (aα3 - bα2 - 3cα - d) (bd - c2) = 0
∴ Either b, c, d in G.P. or α is root of ax3 - bx2 - 3cx - d = 0
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