Polynomials. Yet Again
⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ p ( 1 ) = 1 p ( 2 ) = 3 p ( 3 ) = 5 p ( 4 ) = 7 p ( 5 ) = 9
Let p ( x ) be a polynomial of degree 5 with leading coefficient as 2009 such that the satisfy the equations above, find the value of p ( 6 ) .
The answer is 241091.
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2 solutions
Moderator note:
Nice standard approach.
Bonus question : What would the answer be if I have following equations instead
p ( 1 ) = 5 , p ( 2 ) = 1 , p ( 3 ) = 5 , p ( 4 ) = 1 , p ( 5 ) = 5 ?
Good standard approach.Done similarly.Just replace x with 6 in 5 th line.
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Yes, Standard approach! :D
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Isn't it from the FIITJEE module?
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@Anik Mandal – Lol, Yes :P
But I decided to post it as this was a good question. I personally liked it. The others were kind of easy.
And:- Nice observation ;)
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@Mehul Arora – :P..So you prepared for the phase test? (on the 13th most probably)
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@Anik Mandal – 13th and 14th for me! Eee, Yeah, But Bio is eating my head :3
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@Mehul Arora – Yep same here! I think sst will be hard!
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@Anik Mandal – As far as my preparation is concerned:-
Maths, MAT, Physics:- Piece of cake.
Chemistry, SST:- Almost done, Just have to revise.
Bio:- |-_-| < This expressed it all.
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@Mehul Arora – Ok! Best of luck for the test
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@Anik Mandal – Thanks! How is your preparation?
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@Mehul Arora – Ya almost done except for chem which i dislike.(don't hate.. :P)
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@Anik Mandal – Man! How do you dislike Chemistry? It's a beautiful Subject!
@Mehul Arora – sir you are in which class presently
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@Deepansh Jindal – Don't call me sir, I'm in class 10.
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@Mehul Arora – so what was your rank in tallentex and ftre in class 9th i.e last year???
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@Deepansh Jindal – I didn't appear for Talentex, but I got rank AIR 86 in FTRE.
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@Mehul Arora – nice have you appeared in nsejs i.e ijso???
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@Deepansh Jindal – I did, didn't qualify. didn't prepare for it all that much.
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@Mehul Arora – was your name in mas list ...??
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@Deepansh Jindal – I dunno, I didn't check the MAS list
What was your rank in FTRE?
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@Mehul Arora – it was around 112 ???
@Mehul Arora – did you appear in resostart..??
Similar method!!!
Our fiitjee is the slowest. We will have our phase test in mid july. I too believe bio is the biggest hurdle!!
From the polynomial, We can say that
p ( x ) = 2 0 0 9 ( x − 1 ) ( x − 2 ) ( x − 3 ) ( x − 4 ) ( x − 5 ) + 2 x − 1 (Because the leading coefficient is 2009)
Replacing the value of x by 6, We get:-
p ( 6 ) = 2 0 0 9 ( 6 − 1 ) ( 6 − 2 ) ( 6 − 3 ) ( 6 − 4 ) ( 6 − 5 ) + 2 x − 1
= 2 0 0 9 × 1 2 0 + 1 1
= 2 4 1 0 9 1
Cheers!