One of the roots of | array ccc x+a & b & c a & x+b & c a & b & x+c array |=0 is

Step-by-step solution

aligned & | array ccc x+a & b & c a & x+b & c a & b & x+c array |=0 & (x+a)[(x+b)(x+c)-b c]-b[a(x+c)-a c] & +c[a b-a(x+b)] & =(x+a) [x^2+x c+b x+b c-b c ]-b[a x+a c-a c] & +c[a b-a x-a b] & =(x+a) [x^2+x c+b x ]-a b x-a c x & =x^3+x^2 c+b x^2+a x^2+a c x+a b x-a b x-a c x & =x^3+x^2 c+b x^2+a x^2 & =x^2(x+a+b+c) aligned Now, x^2(x+a+b+c)=0 aligned & x+a+b+c=0 & x=-a-b-c aligned Hence, one of the root is -(a+b+c) .