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#1 2013-04-26 13:27:24

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Quadratic Polynomial and its Factors

If

is a factor of the polynomials
and
, prove 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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#2 2013-04-26 13:44:10

Nehushtan
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Registered: 2013-03-09
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Re: Quadratic Polynomial and its Factors

You mean
is a factor. Hint:

If you let

and
then
and
.


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#3 2013-04-26 14:58:51

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: Quadratic Polynomial and its Factors

That is the problem (n-k) is the factor


'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 2013-04-26 20:29:13

bob bundy
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Registered: 2010-06-20
Posts: 6,311

Re: Quadratic Polynomial and its Factors

hi Agnishom,

I suggest you check the question.  If it started " x + k is a factor....." then that result can be found using Nehushtan's method.

If we maintain (n-k) then since both quadratics must have factors of the form (x - a) and (x - b) that suggests x = n or x = k.  The problem then de-generates and certainly doesn't give that result.

Bob


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

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#5 2013-04-26 20:57:17

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,916
Website

Re: Quadratic Polynomial and its Factors

Maybe that is a printing mistake?

My teacher told to assume (n-k) as a zero of the polynomial


'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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