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#1 2014-04-04 13:19:48

harrychess
Member
Registered: 2014-04-04
Posts: 33

Quadratic Inequalities

Find all values of p such that 2(x+4)(x-2p) has a minimum value of -18.

How do you work this problem?dunno

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#2 2014-04-04 13:47:26

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2014-04-04 13:53:46

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,961
Website

Re: Quadratic Inequalities

Hi bobbym;

What does

p \[Element] 
  Reals && ((x < -4 && p <= (-9 + 4 x + x^2)/(8 + 2 x)) || 
   x == -4 || (x > -4 && p >= (-9 + 4 x + x^2)/(8 + 2 x)))

mean?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2014-04-04 13:55:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

Check post #2. That code is incomplete.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2014-04-04 13:57:27

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,961
Website

Re: Quadratic Inequalities

How did you do that?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#6 2014-04-04 13:57:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

The experimental way of course.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#7 2014-04-04 14:02:36

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,961
Website

Re: Quadratic Inequalities

I hope you do not mean plugging in random numbers!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#8 2014-04-04 14:04:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

Hahhahahahhaahhahahah! Oh Mr. Chattopadhyay you are in rare form today. Thank you, I needed to laugh and that was funny.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9 2014-04-04 14:12:41

ShivamS
Member
Registered: 2011-02-07
Posts: 3,438

Re: Quadratic Inequalities

I am getting p=-5 with the p=1 bobbym got,

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#10 2014-04-04 14:13:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

Very good answer!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11 2014-04-04 14:14:24

ShivamS
Member
Registered: 2011-02-07
Posts: 3,438

Re: Quadratic Inequalities

Are you getting any other possibility?

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#12 2014-04-04 14:17:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

I am looking for something else but so far no.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#13 2014-04-04 14:18:26

ShivamS
Member
Registered: 2011-02-07
Posts: 3,438

Re: Quadratic Inequalities

Agnishom wrote:

I hope you do not mean plugging in random numbers!

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#14 2014-04-04 19:36:50

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,961
Website

Re: Quadratic Inequalities

In[1]:= 2 (x + 4) (x - 2 p)

Out[1]= 2 (4 + x) (-2 p + x)

In[2]:= \!\(
\*SubscriptBox[\(\[PartialD]\), \(x\)]\((2\ \((4 + 
     x)\)\ \((\(-2\)\ p + x)\))\)\)

Out[2]= 2 (4 + x) + 2 (-2 p + x)

In[3]:= Solve[% == 0, x]

Out[3]= {{x -> -2 + p}}

In[4]:= 2 (4 + x) (-2 p + x) /. {{x -> -2 + p}}

Out[4]= {2 (-2 - p) (2 + p)}

In[8]:= Solve[2 (-2 - p) (2 + p) == -18, p]

Out[8]= {{p -> -5}, {p -> 1}}

For harrychess:

Let f(x) = 2 (x + 4) (x - 2 p)
Let f'(x) be the derivative of f(x) with respect to x [,i.e, 2 (4 + x) + 2 (-2 p + x)]
Let g(p) be a polynomial in terms of p which satisfies the equation f'(x) = 0 [,i.e, x = p - 2]
Find p such that 2 (g(p) + 4) (g(p) - 2p) = -18 [,i.e, Solve this, 2 ( 4+ (p-2)) ((p-2)-2p)=-18]


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#15 2014-04-05 12:57:54

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,961
Website

Re: Quadratic Inequalities

Hi bobbym,

Is the above experimental enough?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#16 2014-04-05 13:33:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

I did it in a similar way but there is a shorter way to do the problem I think.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#17 2014-04-05 15:13:25

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,819

Re: Quadratic Inequalities

I found solutions for these:

p=-7
p=-5
p=1
p=3

View Image: Quadratic inequalities.png

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#18 2014-04-05 15:49:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

Hi phrontister;

Did you test that in geogebra?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#19 2014-04-06 02:11:30

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,819

Re: Quadratic Inequalities

No, I didn't think of it.

So now I've entered the x and p coordinates into G and got the result as per image, but I don't know what to do next.

A straight-line connector isn't going to give any solutions, which I suppose means that I need to fit a curve, probably a separate one for ABC and DEF (I'm only guessing). However, I tried that and failed, except with 3-point circles through ABC and DEF...from which I don't get any other solutions either.

In fact, I think there are no non-integer solutions, and my spreadsheet seems to indicate that my integer solutions are the only answers to this puzzle.

View Image: QInequalities(G).png

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#20 2014-04-06 03:17:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

Hi phrontister;

There are only 2 answers for p.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#21 2014-04-06 04:07:43

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,819

Re: Quadratic Inequalities

Hi Bobby,

I got 4 answers for p (ie, -7, -5, 1 and 3):

p = -7 and x = -13.....2(-13+4)(-13-2*-7) = -18
p = -7 and x = -5.......2(-5+4)(-5-2*-7) = -18
p = -5 and x = -7.......2(-7+4)(-7-2*-5) = -18
p = 1 and x = -1........2(-1+4)(-1-2*1) = -18
p = 3 and x = -3........2(-3+4)(-3-2*3) = -18
p = 3 and x = 5.........2(5+4)(5-2*3) = -18

Did I misunderstand something about the question, or make an error?


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#22 2014-04-06 04:12:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

Hi;

You can check these quickly with geogebra.

When p = - 7 the minimum is - 50

When p = 3 the minimum is - 50


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#23 2014-04-06 04:25:08

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,819

Re: Quadratic Inequalities

Oops! I overlooked the word 'minimum! >facepalm<

Yes...there are only solutions 1 and -5.


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#24 2014-04-06 04:29:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,549

Re: Quadratic Inequalities

Misheeru is the facepalm kid. I can not deal with two of ya. My brain is exploding.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#25 2014-04-06 04:38:27

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,819

Re: Quadratic Inequalities

Yes, I learnt that term from Misheeru, and I felt the need to use it now!

I've been trying to use G with this, but am getting nowhere. So far I've entered the two {x,p} coordinates and drawn a line through them, but I've run out of ideas....and I may be on the wrong track doing that, anyway.


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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