DeterminantHard
Question
The determinant 
is equal to zero, then
is equal to zero, then Options
A.a, b, c are in AP
B.a, b, c are in GP
C.a, b, c are in HP
D.(x - α) is a factor of ax2 + 2bx + c
Solution
Given, 
Applying C3 → C3 - (αC1 + C2)
;
⇒ - aα2 + 2bα + c)(ac - b2) = 0
⇒ aα2 + 2bα + c = 0 or b2 = ac
⇒ x - α is a factor of ax2 + 2bx + c
or a, b, c are in GP.
Applying C3 → C3 - (αC1 + C2)
;
⇒ - aα2 + 2bα + c)(ac - b2) = 0
⇒ aα2 + 2bα + c = 0 or b2 = ac
⇒ x - α is a factor of ax2 + 2bx + c
or a, b, c are in GP.
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