The determinant |a b aalpha+bb c balpha+...

The determinant `|a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0,` if `a ,b , c` are in A.P. `a ,b ,c` are in G.P. `a ,b ,c` are in H.P. `alpha` is a root of the equation `a x^2+b c+c=0` `(x-alpha)` is a factor of `a x^2+2b x+c`

Similar Questions

Explore conceptually related problems

If a,b,c, are in A.P., b,c,d are in G.P. and c,d,e, are in H.P., then a,c,e are in

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

If a,b,c are in A.P. then the roots of the equation (a+b-c)x^2 + (b-a) x-a=0 are :

the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha+c,,0):}|=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

If a,b,c are in A.P., a,x,b are in G.P. and b,y,c are in G.P. then a^(2),b^(2),y^(2) are in