Suppose `a ,b ,c in I`such that the greatest common divisor fo `x^2+a x+ba n dx^2b x+ci s(x+1)`and the least common ultiple of `x^2+a x+ba n dx^2+b x+c`is `(x^3-4x^2+x+6)dot`Then the value of `|a+b+c|`is equal to ___________.

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Correct Answer – 6

`x^(2)+ax+b-=(x+1)(x+b)rArrb+1=a” “(1)`

also `x^(2)+bx+c-=(x+1)(x+c)rArrc+1=b`

or `b+1=c+2″ “(2)`

Hence `b+1=a=c+2`

Also `(x+1)(x+b)(x+c)-=x^(3)-4x^(2)+x+6`

`rArrx^(3)+(1+b+c)x^(2)+(b+bc+c)x+bc-=x^(3)-4x^(2)+x+6`

`rArr1+b+c=-4`

`rArr 2c+2=-4`

`rArr c=-3,b=-2 and a =-1`

`rArr a+b+c=-6`