|[a,b,a alpha+b],[b,c,b alpha+c],[a alpha+b,b alpha+c,0]|=0," if "a,b,c" are in: "

If the determinant |[a,b,2a alpha+3b],[b,c,2b alpha+3 c],[2a alpha+3b,2b alpha+3c,0]|=0 then

If det[[a,b,a alpha+bb,c,b alpha+ca 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 |(a,b,a alpha+b),(b,c, b alpha+c),(a alpha+b, b alpha+c,0)|=0 then

Show that abs((a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0):} =0 if alpha is not the root of the equation (ax^2+2bx+c)=0 then a,b,c are in G.P.

The system of equations ax+by+(a alpha+ b)z=0 bx+cy+(b alpha+c)z=0 (a alpha+b)x+(balpha+c)y=0 has a non zero solutions if a,b,c are in

Given that a alpha^(2)+2b alpha+c!=0 and that the system of equations (a alpha+b)x+alpha y+bz=0,(b alpha+c)x+by+cz=0,(a alpha+b)y+(b alpha+c)z=0 has a non trivial solution,then a ,b,c are in

The determinant Delta = |(b,c,b alpha +c),(c,d,c alpha + d),(b alpha + c,c alpha + d,a a^(3) - c alpha)| is equal to zero, if