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

Options

A. (a)`x`
B. (b)`-x`
C. (c)`-1`
D. (d)`1`

Answer

C

Explanation

`(c )` `|{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c):}|`
Applying `R_(1)toR_(1)-2R_(2)+R_(3)`
`|{:(0,0,1),(x+2,x+3,x+b),(x+3,x+4,x+c):}| ( :' a-2b+c=1)`
Applying `R_(3)toR_(3)-R_(2)`,
the determinant reduces to
`|{:(0,0,1),(x+2,x+3,x+b),(1,1,c-b):}|=-1`