The constant term of the polynomial | array ccc x+3 & x & x+2 x & x+1 & x-1 x+2 & 2 x & 3 x+1 array | is

Step-by-step solution

| array ccc x+3 & x & x+2 x & x+1 & x-1 x+2 & 2 x & 3 x+1 array |=f(x) Applying R ₂ R ₂- R ₁ and R ₃ R ₃- R ₁ f(x)= | array ccc x+3 & x & x+2 -3 & 1 & -3 -1 & x & 2 x-1 array | Applying C ₁ C ₁- C ₃ and C ₂ C ₂- C ₃ f(x)= | array ccc 1 & -2 & x+2 0 & 4 & -3 -2 x & 1-x & 2 x-1 array | Expand w.r.t. ' C ₁ , f(x)=[4(2 x-1)+3(1-x)] +(-2 x )[6-4( x +2)] f(x)=[8 x-4+3-3 x]+[-2 x][-4 x-2]f(x)=(5 x-1)+ (8 x²+4 x ) f(x)=8 x²+9 x-1 Hence, the constant term of quadratic equation is -1 .