If | array lll x +1 & x +2 & x + a x +2 & x +3 & x + b x +3 & x +4 & x + c array |=0 , then a, b, c are

Step-by-step solution

Given, | array lll x+1 & x+2 & x+a x+2 & x+3 & x+b x+3 & x+4 & x+c array |=0 Applying R ₁ R ₁+ R ₃-2 R ₂ , we get aligned & | array ccc 0 & 0 & a+c-2 b x+2 & x+3 & x+b x+3 & x+4 & x+c array |=0 & (a+c-2 b) [x²+6 x+8- (x²+6 x+9 ) ] & (a+c-2 b)(-1)=0 & 2 b=a+c & a, b, c are in AP. aligned