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anchit saini (4396)

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$f(x) = (x-3)P(x) + 15 ................1 \\ \\ f(x) = (x-1)^2 Q(x) + 2x + 1 ...............2\\ \\ f(x) = (x-1)^2(x-3) R(x) + ax^2 + bx + c ...............3 \\ \\ \mbox{ where P(x),Q(x),R(x) are arbitrary functions while the}\\ \\ \mbox{ remainder in eqn 3 is taken to be a quadratic as}\\ \\ \mbox{ the function is divided by a cubic . }\\ \\ \mbox{In eqn 3 } \\ \\ f(1)=a+b+c \\ \\ =3 \mbox{ from eqn 2} \\ \\ f(3)=9a + 3b + c \\ \\ =15 \mbox{ from eqn 1} \\ \\ \mbox{Differentiating eqn 1 , we get } \\ \\ f$

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