Math Is Fun Forum

Oran2009

Member

Registered: 2016-06-13

Posts: 21

Some Polynomial Problems

1) The polynomial

is divisible by $x-4$ and all of its zeroes are integers. Find all possible values of $m$.

     
     Do I plug in x=4? What would I do???
-------------------------------------------------------------------------------------------------------------------------------------------
2) Suppose the polynomial

is of degree

and satisfies

,

,

, and

.

Determine the value of

.

     
     How to do this?
-------------------------------------------------------------------------------------------------------------------------------------------

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Some Polynomial Problems

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Oran2009

Member

Registered: 2016-06-13

Posts: 21

Re: Some Polynomial Problems

I got #1. The answer is just m=5

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Some Polynomial Problems

Last edited by thickhead (2017-02-07 19:19:24)

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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.}

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: Some Polynomial Problems

Hi;
I am suffering from a migraine so I am a bit weak....

What is migraine?

Last edited by iamaditya (2017-02-07 23:56:12)

---

Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Some Polynomial Problems

Hi;

Without the jargon, it is an intense headache.

The symptoms that one is on the way are bad enough.

http://www.health.com/health/gallery/0, … 78,00.html

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Some Polynomial Problems

I feel very sorry for bobbym having my grain.

---

{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.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Some Polynomial Problems

Thanks, but it is the consequence of doing all that EM.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: Some Polynomial Problems

EM...means??

---

Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Some Polynomial Problems

I am glad you asked me that question. EM mean Experimental Mathematics.

I would say the first rule is this:

Get Your Hands Dirty: This is easy and fun to do. Stay loose and experiment. Plug in lots of numbers. Keep playing around until you see a pattern. Then play around some more, and try to figure out why the pattern you see is happening. It is a well-kept secret that much high-level mathematical research is the result of low-tech "plug and chug" methods. The great Gauss, widely regarded as one of the greatest mathematicians in history, was a big fan of this method. In one investigation, he painstakingly computed the number of integer solutions to x^2 + y^2 < 90,000

Today, we can be assisted by a computer to help with this type of research.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Some Polynomial Problems

1) The polynomial

is divisible by $x-4$ and all of its zeroes are integers. Find all possible values of $m$.

     
     Do I plug in x=4? What would I do???
-------------------------------------------------------------------------------------------------------------------------------------------
2) Suppose the polynomial

is of degree

and satisfies

,

,

, and

.

Determine the value of

.

     
     How to do this?
-------------------------------------------------------------------------------------------------------------------------------------------

Hi Oran2009,
I have come out with an easier solution for (2) in which you don't have to solve simultaneous equations.
Try the polynomial f(x)=A(x-3)(x-4)(x-5)+B(x-3)(x-4)+C(x-3)+2
The remainder 2 for the division by x-3 is already incorporated.
Plug in x=4 you get C.
Plug in x=5you get B.
Plug in x=6 you get A.
then plug in x=0 to get f(0).
Even if it is homework problem lot of time has elapsed and I am giving you only method.

---

{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.}