Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

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

'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 have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,786

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)*

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

Offline

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,786

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

Offline

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,889

Highest common factor, I'd presume?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,786

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,786

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

Offline

I really do not understand what the dilemma is.

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

Pages: **1**