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

Agnishom
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From: The Complex Plane
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Quadratic Polynomial and its Factors

If

is a factor of the polynomials
and
, prove that


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#2 2013-04-26 13:44:10

Nehushtan
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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'
'You made a human being happy! There is no further achievement.' -bobbym

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#4 2013-04-26 20:29:13

bob bundy
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Registered: 2010-06-20
Posts: 6,421

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


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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: 17,134
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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'
'You made a human being happy! There is no further achievement.' -bobbym

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