The system of equations \[ \begin{array}{l} (a \alpha+b) x+a y+b z=0 \\ (b \alpha+c) x+b y+c z=0...

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The system of equations
\[
\begin{array}{l}
(a \alpha+b) x+a y+b z=0 \\
(b \alpha+c) x+b y+c z=0 \\
(a \alpha+b) y+(b \alpha+c) z=0
\end{array}
\]
has a non-trival solution, if
(a) \( a, b, c \) are in A.P
(b) \( a, b, c \) are in G.P
(c) \( a, b, c \) are in H.P
(d) \( \alpha \) is a root of \( a x^{2}+2 b x+c+1=0 \)
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