If `|(a,b,aalpha+b),(b,c,balpha+c),(a alpha+b,b alpha+c,0)|=0` then

If |(a,b,a alpha+b),(b,c, b alpha+c),(a alpha+b, b alpha+c,0)|=0 then

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

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

If alpha ne 0 and a,b,c are in G.P., show that : |(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0

If |{:(a, b, aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c," "0):}|=0 then

The determinant : |(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0 if :

If the determinant |(a ,b,2aalpha+3b),(b, c,2balpha+3c),(2aalpha+3b,2balpha+3c,0)|=0 then (a) a , b , c are in H.P. (b) alpha is root of 4a x^2+12 b x+9c=0 or(c) a , b , c are in G.P. (d) a , b , c , are in G.P. only a , b ,c are in A.P.

the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha+c,,0):}|=0 is equal to zero if

the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha+c,,0):}|=0 is equal to zero if

the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha+c,,0):}|=0 is equal to zero if