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

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,aalpha-b),(b,c,balpha-c),(2,1,0):}|=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

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

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|

The value of the determinant |{:(a, b,0), (0,a, b),(b,0,a):}| is equal to- a. a^3-b^3 b. a^3+b^3 c. 0 d. none of these

The value of the determinant |(b +c,a -b,a),(c +a,b -c,b),(a +b,c -a,c)| , is

If |{:(4,-4,0),(a,b+4,c),(a,b,c+4):}|=0 , then a+b+c is equal to

Use properties of determinants to solve for x: |{:(,x+a,b,c),(,c,x+b,a),(,a,b,x+c):}|=0 and x=0