Find the value of x

Question

a b ax+b
b c bx+c = 0
ax+b bx+c c
Find value of x in this determinant
This is a 3X3 determinant which is equal to zero.

A detailed working is expected.

Answer 1

Use the rule for computing the value of a determinant.  Sarrus' rule might be most useful (that's the one that makes an array 3 by 5, in which the last two columns are duplicates of the first two columns of the 3 by 3 matrix). Then you multiply 3 terms from each diagonal that goes through the array (along lines that go through the array from upper left to lower right, and sum those 3 products, and then do a similar calculation along diagonals going from upper right to lower left...the determinant value is the difference of those two sums.

 

You'll get a lot of Algebra! Set this determinant value to 0 and solve the equation. Good luck.