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If |(a,b,aalpha+b),(b,c,balpha+c),(aalph...

If `|(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0,` prove that a,b,c, are in G.P. or `alpha` is a root of `ax^(2)+`2bx+c=0

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If |{:(a,b,a alpha+b),(b,c,b alpha+c),(a alpha +b,b alpha+c,0):}|=0 Prove that a,b,c are in G.P. or alpha is a root of ax^2 + 2bx + c=0

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