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Differential Calculus

Blazing goIITian

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22 Jul 2008 09:20:00 IST

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831

Method please :)

None

A polynomial f(x) leaves remainder 15 when divided by (x-3) and 2x+1 when divided by (x-1)^2.

Find the remainder when it is divided by (x-1)^2 * (x-3).

I do have a method , but still i think more than one approach maybe a distinct possibility :)

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Comments (4)

Gaurav |spideyunlimited| Ragtah

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Joined: 16 Dec 2006

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30 Jul 2008 16:36:41 IST

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Anyone? Even I can't recollect.

Rahul Raghavendra

Blazing goIITian

Joined: 9 Jan 2008

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30 Jul 2008 17:15:27 IST

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Is the answer

15 or 3

anchit saini

Blazing goIITian

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4 Aug 2008 13:38:42 IST

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

Rahul Raghavendra

Blazing goIITian

Joined: 9 Jan 2008

Posts: 843

4 Aug 2008 16:40:08 IST

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Oh i made a mistake nice one , thanks

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