Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
Pages: 1
#1 2014-04-06 18:16:56
Polynomials - GCD
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'
I'm not crazy, my mother had me tested.
Offline
#2 2014-04-06 20:17:45
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
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 (2014-04-07 02:02:46)
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
Offline
#3 2014-04-07 00:44:52
Re: Polynomials - GCD
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'
I'm not crazy, my mother had me tested.
Offline
#4 2014-04-07 02:00:17
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
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 (2014-04-07 02:08:08)
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#5 2014-04-07 03:44:15
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'
I'm not crazy, my mother had me tested.
Offline
#6 2014-04-07 03:46:56
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Polynomials - GCD
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
#7 2014-04-07 03:48:07
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
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 (2014-04-07 03:48:45)
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#8 2014-04-07 03:56:18
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
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 ..... 
hope you're still following this ...
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#9 2014-04-07 04:06:20
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'
I'm not crazy, my mother had me tested.
Offline
Pages: 1