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#1 2014-04-06 18:16:56

Agnishom
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Polynomials - GCD

If (x+a) is the HCF of x^2 + px + q and x^2 +lx + m then solve for a


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#2 2014-04-06 20:17:45

bob bundy
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Registered: 2010-06-20
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Re: Polynomials - GCD

hi Agnishom,

Suppose (x+b) and (x+c) are the other factors of the quadratics. 

ie. (x+a)(x+b) = x^2 + px + q

and

(x+a)(x+c) = x^2 + Lx + m

Then

ab = q and ac = m        =>       b = qc/m

also

a+b =  p and a+c =  L

So substitute for b (in terms of c) and then eliminate c from these equations.  Make a the subject of the equation that is left.

Bob

Last edited by bob bundy (2014-04-07 02:02:46)


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#3 2014-04-07 00:44:52

Agnishom
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Re: Polynomials - GCD

bob bundy wrote:

So substitute for b (in terms of c) and then eliminate c from these equations.  Make a the subject of the equation that is left.

Bob

Can it be done? How?


'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 2014-04-07 02:00:17

bob bundy
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Re: Polynomials - GCD

Can it be done? How?

Comme si:

Dividing

Also

and

Subtracting

Bob

ps.  Not sure what HCF means anyway.  The above holds for any repeated factor.

You could litter the above with provisos like q ≠ 0, but there's no need as the quadratics 'collapse' if any such conditions fail to apply.

Last edited by bob bundy (2014-04-07 02:08:08)


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

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#5 2014-04-07 03:44:15

Agnishom
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From: The Complex Plane
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Re: Polynomials - GCD

Brilliant!

Thank You.

HCF means GCD


'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 2014-04-07 03:46:56

anonimnystefy
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Re: Polynomials - GCD

Highest common factor, I'd presume?


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#7 2014-04-07 03:48:07

bob bundy
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Registered: 2010-06-20
Posts: 6,338

Re: Polynomials - GCD

HCF means GCD

I worked that out.  But what does 'greatest' or 'highest' mean in the context of a factorisation of a quadratic.

(x+a) > (x+b)  ?????

I think the question should just read


If (x+a) is a factor of x^2 + px + q and x^2 +lx + m ..............................

Bob

Last edited by bob bundy (2014-04-07 03:48:45)


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

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#8 2014-04-07 03:56:18

bob bundy
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Registered: 2010-06-20
Posts: 6,338

Re: Polynomials - GCD

Yes Highest Common Factor = Greatest Common Divisor.  but what's it doing in this question ?

HCF is a significant bit of maths for me.  It's when I discovered that I cannot learn anything by hearing it .... I just get audio blindness .......I have to see it.  My first high school maths lesson went badly because all the teacher did was talk HCF and LCM and I was hopelessly confused.  So I took the text book out for lunch and taught myself what it was all about.  It's a milestone in my mathematical education; 

ie.

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

In my case it was me that helped me rather than the teacher ..... dizzy  hope you're still following this ... smile

Bob


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

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#9 2014-04-07 04:06:20

Agnishom
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From: The Complex Plane
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Re: Polynomials - GCD

I really do not understand what the dilemma is.


'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

Online

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