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

Correct Answer is : Geometric progression

Arithmetico-geometric progression

AP EAMCET Engineering 2012 Solved Paper

Section: Mathematics

Question : 135 of 160

Marks: +1, -0

Given that, aα2+2bα+c≠0 and that the system of equations
(aα+b)x+ay+bz=0
(bα+c)x+by+cz=0
(aα+b)y+(bα+c)z=0
has a non-trivial solution, then a,b and c lie in

Arithmetic progression
Geometric progression
Harmonic progression
Arithmetico-geometric progression

Validate

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aα+b	a	b
bα+c	b	c
0	aα+b	bα+c

aα+b	a	b
bα+c	b	c
−(aα2+2bα+c)	0	0