The function f(x)=ax^3+bx^2+7x+6 has a remainder or 6 when divided by x-1 and is exactly divisible by x-2.Find the values of a and b?

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Answer 1 · 2018-02-20T17:57:55

# a=2, and b=-9#.

By the Remainder Theorem, when the poly. #f(x)# is divided by

#(x-1)#, the remainder is #f(1)#.

#:. f(1)=6 rArr a+b+7+6=6 rArr a+b=-7......(1)#.

As #f(x)# is exactly divisible by #(x-2)#, the remainder #f(2)=0#.

#rArr a(2)^3+b(2)^2+7(2)+6=0#.

#:. 8a+4b=-20, or, 2a+b=-5............................(2)#.

#:. (2)-(1) rArr a=2," and, then, by "(1), b=-9#.