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`

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,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 roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

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.

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. alpha is root of 4a x^2+12 b x+9c=0 or a , b , c are in G.P. a , b , c , are in G.P. only a , b ,c are in A.P.

If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P. c. H.P. d. none of these

If x ,ya n dz are in A.P., a x ,b y ,a n dc z in G.P. and a ,b ,c in H.P. then prove that x/z+z/x=a/c+c/a .

If a^2+b^2,a b+b c and b^2+c^2 are in G.P., then a ,b ,c are in a. A.P. b. G.P. c. H.P. d. none of these

If a^2+b^2,a b+b c ,a n db^2+c^2 are in G.P., then a ,b ,c are in a. A.P. b. G.P. c. H.P. d. none of these