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Differential Calculus

anchit saini's Avatar
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22 Jul 2008 09:20:00 IST
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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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Gaurav |spideyunlimited| Ragtah's Avatar

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30 Jul 2008 16:36:41 IST
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Anyone? Even I can't recollect.
Rahul Raghavendra's Avatar

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30 Jul 2008 17:15:27 IST
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Is the answer


 


15 or 3

anchit saini's Avatar

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4 Aug 2008 13:38:42 IST
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f(x) = (x-3)P(x) + 15 ................1 \\ \\<br/>f(x) = (x-1)^2 Q(x) + 2x + 1 ...............2\\ \\<br/>f(x) = (x-1)^2(x-3) R(x) + ax^2 + bx + c ...............3 \\ \\<br/>\mbox{ where P(x),Q(x),R(x) are arbitrary functions while the}\\ \\<br/>\mbox{ remainder in eqn 3 is taken to be a quadratic as}\\ \\<br/>\mbox{ the function is divided by a cubic . }\\ \\<br/>\mbox{In eqn 3 } \\ \\<br/>f(1)=a+b+c \\ \\<br/>=3 \mbox{ from eqn 2} \\ \\<br/>f(3)=9a + 3b + c \\ \\<br/>=15 \mbox{ from eqn 1} \\ \\<br/>\mbox{Differentiating eqn 1 , we get } \\ \\<br/>f

Rahul Raghavendra's Avatar

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4 Aug 2008 16:40:08 IST
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Oh i made a mistake nice one , thanks



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