If `a ne b ne c`, then solution of equation
`|{:(x-a,x-b,x-c),(x-b,x-c,x-a),(x-c, x-a,x-b):}|=0" "is:`

Solve the equation |{:(x+a,x+b,x+c),(x+b,x+c,x+a),(x+c,x+a,x+b):}|=0

If a,b,c, in R, find the number of real root of the equation |{:(x,c,-b),(-c,x,a),(b,-a,x):}| =0

both roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are

If f(x)=|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}| , then

If a,b,c are real, then both the roots of the equation (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are always (A) positive (B) negative (C) real (D) imaginary.

If the roots of the equation (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are equal then

if a+b+c=0 then Delta=|{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 is

The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are different) is satisfied by (A) x=(a+b+c0 (B) x= 1/3 (a+b+c) (C) x=0 (D) none of these

If |1 1 1a b c a^3b^2c^3|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b ,c are different, then the determinant |1 1 1(x-a)^2(x-b)^2(x-c)^2(x-b)(x-c)(x-c)(x-a)(x-a)(x-b)| vanishes when a. a+b+c=0 b. x=1/3(a+b+c) c. x=1/2(a+b+c) d. x=a+b+c

If a , b , c , are roots of the equation x^3+p x+q=0, prove that |[a ,b, c],[ b ,c, a],[ c, a, b]|=0