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Q.

If the remainders of the polynomial f(x) when divided by x – 1, x – 2 are 2, 5 then the remainder of f(x) when divided by (x–1)(x– 2) is

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a

0

b

1 – x

c

2x–1

d

3x–1

answer is D.

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Detailed Solution

f(x)=(x−1)(x−2)+ax+b f(1)=2⇒a+b=2f(2)=5⇒2a+b=5⇒a=3,   b=−1Remainder is 3x−13x-1
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If the remainders of the polynomial f(x) when divided by x – 1, x – 2 are 2, 5 then the remainder of f(x) when divided by (x–1)(x– 2) is