Question

using determinants show that x=2 is the root of the equation

x -6 -1

2 -3x x-3 =0 and hence solve it completely

3 2x x+2

Answer 1

Even your question is not clear, I have
Solved it in the attachment.
I have applied factor theorem to solove
this equation.

Factor theorem says :
If each element of a determinant is a polynomial in x and it vanishes when
we put x = a then (x-a) is a factor of the
determinant.
.
.
Karups