## polynomial

- Abdul Muntakim Rafi
**Posts:**173**Joined:**Tue Mar 29, 2011 10:07 pm**Location:**bangladesh,the earth,milkyway,local group.

### polynomial

$p(7)=77,p(x)=85(x$ is greater than $7)$; what's the root of $p(n)$?

### Re: polynomial

Let $q(x)=p(x)-85$. Then $q(x)=0$ for all $x>7$, i.e. $q$ has infinitely many roots. So $q$ must be the zero polynomial, which implies $p(x)=85$ for all $x$.

"Everything should be made as simple as possible, but not simpler." - Albert Einstein

- Abdul Muntakim Rafi
**Posts:**173**Joined:**Tue Mar 29, 2011 10:07 pm**Location:**bangladesh,the earth,milkyway,local group.

### Re: polynomial

Bhaiya, $p(x)=85$ for a certain value greater than $7$ (not just any value greater than $7$) ...

**Man himself is the master of his fate...**

### Re: polynomial

$p(x)=11x$

$p(x)=10x+7$

$p(x)=12x-7$

$\dots$

All these polynomials satisfy your conditions, and have different roots. So I don't really know what you're asking for.

$p(x)=10x+7$

$p(x)=12x-7$

$\dots$

All these polynomials satisfy your conditions, and have different roots. So I don't really know what you're asking for.

"Everything should be made as simple as possible, but not simpler." - Albert Einstein

- nafistiham
**Posts:**829**Joined:**Mon Oct 17, 2011 3:56 pm**Location:**24.758613,90.400161-
**Contact:**

### Re: polynomial

Are you wishing to get such a polynomial, that satisfies $77$ for $7$, and $85$ for a definite integer greater than $7$ ?

Won't there be various such polynomials ?

Won't there be various such polynomials ?

\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]

Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

- Abdul Muntakim Rafi
**Posts:**173**Joined:**Tue Mar 29, 2011 10:07 pm**Location:**bangladesh,the earth,milkyway,local group.

### Re: polynomial

The ques was like this-

Two guys were talking... One said hey my age is the root of a polynomial.. Seeing the polynomial equation $P(n)$ the other said your age is $7$... But he figured it was wrong cause $p(7)=77$ ... The first guy said yes u r wrong... my age is greater than $7$... Then he guessed a number greater than $7$ ... That gave him $p(x)=85$...

Now what's his age?

Two guys were talking... One said hey my age is the root of a polynomial.. Seeing the polynomial equation $P(n)$ the other said your age is $7$... But he figured it was wrong cause $p(7)=77$ ... The first guy said yes u r wrong... my age is greater than $7$... Then he guessed a number greater than $7$ ... That gave him $p(x)=85$...

Now what's his age?

**Man himself is the master of his fate...**