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Given that $a α^{2} + 2 b α + c \neq 0$ and that the system of equations $(a α + b) x + a y + b z = 0, (b α + c) x + b y + c z = 0, (a α + b) y + (b α + c) z = 0$ has non- trivial solution then a,b,c lies in

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Correct option is B

aα+babbα+cbc0aα+bbα+c=0 C1→C1-αC2-C3⇒0ab0bc-aα2+2bα+caα+bbα+c=0-a0+caα2+2bα+c+b0+baα2+2bα+c=0aα2+2bα+c≠0then b2=acA,b,c are in G.P

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Given that aα2+2bα+c≠0and that the system of equations aα+bx+ay+bz=0,bα+cx+by+cz=0,aα+by+bα+cz=0has non- trivial solution then a,b,c lies in

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Given that $a α^{2} + 2 b α + c \neq 0$ and that the system of equations $(a α + b) x + a y + b z = 0, (b α + c) x + b y + c z = 0, (a α + b) y + (b α + c) z = 0$ has non- trivial solution then a,b,c lies in