The number of distinct real roots of | array ccc x & x & x x & x & x x & x & x array | in the interval [ - 4 , 4 ] is

Step-by-step solution

| array lll x & x & x x & x & x x & x & x array |=0 Applying C₁ C₁+C₂+C₃ | array lll 2 x+ x & x & x 2 x+ x & x & x 2 x+ x & x & x array |=0 (2 x+ x) | array lll 1 & x & x 1 & x & x 1 & x & x array |=0 [Applying R₂ R₂-R₁ and R₃ R₃-R₁ , we get (2 x+ x) | array ccc 1 & x & x 0 & x- x & 0 0 & 0 & x- x array |=0 (2 x+ x) [1 ( - x)² ]=0 (2 x+ x)( x- x)²=0 2 x=- x or x= x x=-2 which is not possible as for - 4 x 4 , we get -1 x 1 or x=1 So, x= 4 . Hence, only one real root exist.