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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,020

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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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,020

Can it be done? How?

Comme si:

Dividing

Also

and

Subtracting

Bob

ps. Not sure what **H**CF 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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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

Highest common factor, I'd presume?

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,020

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,020

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.

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

Bob

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I really do not understand what the dilemma is.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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