Question

If `x=-9` is a root of `|(x,3,7),(2,x,2),(7,6,x)|=0` then other two roots are…………………

Answer 1

Given, `|{:(x,3, 7),(2, x, 2),(7, 6, x):}|=0`
Applying `R_(1) to R_(1) + R_(2) + R_(3)`
`rArr |{:(x+9,x+9, x+9),(2, x, 2),(7, 6, x):}|=0 rArr (x+9)|{:(1,1, 1),(2, x, 2),(7, 6, x):}|=0`
Applying `C_(2) to C_(2)-C_(1) " and " C_(3) to C_(3)-C_(1)`
`rArr (x+9)|{:(1,0, 0),(2, x-2, 0),(7, -1, x-7):}|=0 rArr (x+9)(x-2)(x-7) = 0`
`rArr x =-9, 2, 7` are the roots.
`therefore `Other two roots are 2 and 7