" The determinant "Delta=|[a,b,a+b],[b,c,b alpha+c],[a alpha+b,ba+c,0]|" is equal to zero if "

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

The determinant Delta=|(a,b,ax+b),(b,c,bx+c),(ax+b,bx+c,c)| is equal to zero, 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) ax^(2) + bx + c = 0

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

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

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

If det[[a,b,a alpha+bb,c,b alpha+ca alpha+b,b alpha+c,0]]=0 then

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