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**Randy123****Guest**

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 bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,321

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

The sum of coefficients , obviously is

**{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.}**

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

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

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

**{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.}**

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,321

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

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.

**{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.}**

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,321

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**mathicINDIA****Member**- Registered: 2017-06-03
- Posts: 7

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]

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

mathicINDIA wrote:

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

(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha

{Gods rejoice at those places where ladies are respected.}

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