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Randy123

Guest

Polynomial help

Suppose f is a polynomial such that f(0) = 47, f(1) = 32, f(2) = -13, and f(3)=16. What is the sum of the coefficients of f?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Polynomial help

hi Randy123

A polynomial has the form:

You only have 4 constraints so you'd have to assume that a5, a6, .... are all zero.

You can then form 4 equations like this:

I got that one by putting x=2

You'll get three more by putting x=0, x=1 and x=3.

Then you need to use simultaneous equation methods to solve for all the 'a's.

If you can get those equations, but cannot solve them, then post again with your 4 equations.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Polynomial help

The sum of coefficients , obviously is

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Polynomial help

The problem is just a hoax, simply to test presence of mind.

Last edited by thickhead (2017-06-15 21:19:11)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Polynomial help

Hi thickness,

Oh yes!  Silly me. . Obviously, this reveals I have no presence of mind.  In fact, maybe no mind at all.  And it doesn't even have to be cubic

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Polynomial help

I am sorry, bob bundy. I did not mean that.You have had so many wonderful solutions.But when we are preoccupied with some problem, we can't differentiate between tea and coffee. I only hoped you could put x=1 instead of x-2 in your post.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Polynomial help

It's ok.  I wasn't offended.  Just cross with myself for missing that.  There's a phrase for it here in the UK: can't see the wood for the trees.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathicINDIA

Member

Registered: 2017-06-03

Posts: 7

Re: Polynomial help

If 1 & -1 are the zeroes of the polynomial p(x)=Lx^4+Mx^3+Nx^2+Rx+P=0, prove that L+M+P=M+R=0.    [JEE mains 2014, AIEEE 2006, IIT 1998]

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Polynomial help

If 1 & -1 are the zeroes of the polynomial p(x)=Lx^4+Mx^3+Nx^2+Rx+P=0, prove that L+M+P=M+R=0.    [JEE mains 2014, AIEEE 2006, IIT 1998]

I think it should be
If 1 & -1 are the zeroes of the polynomial

, prove that

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}