If f(x)= | array ccc x & x & x x³ & x² & x 2 x & 1 & x array | , then _ n -> f(x) x² is equal to

Step-by-step solution

Given, f ( x )= | array ccc x & x & x x ³ & x ² & x 2 x & 1 & x array | Expanding the determinant along the first row, we get aligned &= x (x³-x )- x (x⁴-2 x² ) &= x (x³-x )- x x² (x²-2 ) &= x (x³-2 x³ ) & . _ x 0 f(x) x² ) x (-x³ ) &= _ x 0 [x x (x²-1 )- x x² (x²-2 ) . x² x² (x²-2 )- x (x³ ) &= _ x 0 x x (x²-1 )- x (x²-2 )- x x &=[1(0-1)- 0(0-2)- 0 0]-[-1+2] &=1 aligned