InterviewSolution
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InterviewSolution
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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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Answer» 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` |
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