Show that `|[x+1,x+2,x+a], [x+2,x+3,x+b],[ x+3,x+4,x+c]|=0` where `a ,\ b ,\ c` are in A.P.

If a,b,c are in AP show that |[x+1,x+2,x+a],[x+2,x+3,x+b],[x+3,x+4,x+c]|=0

Show that [[x-3,x-4,x-alpha],[x-2,x-3,x-beta],[x-1,x-2,x-gamma]]=0 where alpha,beta,gamma are in AP

If f(x) = |[x+a,x+2,x+1],[x+b,x+3,x+2],[x+c,x+4,x+3]| and a - 2b + c = 1 then

If f(x) = |[x+a,x+2,x+1],[x+b,x+3,x+2],[x+c,x+4,x+3]| and a - 2b + c = 1 then

a x a x 3 x b x b x 2 x c x c= .............

If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a], [x+3,x+4,x+2b], [x+4,x+5,x+2c]| is(A) 0 (B) 1 (C) x (D) 2x

If a ,b ,c are different, then the value of |[0,x^2-a, x^3-b],[ x^2+a,0,x^2+c],[ x^4+b, x-c,0]| is a. c b. a c. b d. 0

Let |[x^2+3x,x-1,x+3],[x+1,-2x,x-4],[x-3,x+4, 3x]|=a x^4+b x^3+c x^2+e be an identity in x , where a , b , c , d , e are independent of xdot Then the value of e is (a) 4 (b) 0 (c) 1 (d) none of these

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in Rdot

If x^a=x^(b//2)z^(b//2)=z^c , then prove that 1/a ,1/b ,1/c are in A.P.