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September 4th, 2011, 10:14 AM   #1
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solutions of an equation

1/x - 1/(x+1) - 3

I solve it
and then the solutions are x = (sqrt(21)-3)/6 and x = -(sqrt(21)+3)/6

but my teacher said the number of solutions of an equation depends on the degree of equation

why the equation has up to 2 solution

but it's not a quadratic equation

Can you explain me, please?


Thank you so much
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September 4th, 2011, 10:30 AM   #2
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Re: solutions of an equation

If you mean:





not necessary to put answers to equation and check them instead check the steps that lead you to solve a problem
several times.
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September 4th, 2011, 10:45 AM   #3
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Re: solutions of an equation

Quote:
Originally Posted by versmart
If you mean:





not necessary to put answers to equation and check them instead check the steps that lead you to solve a problem
several times.
my teacher said the number of solutions of an equation depends on the degree of equation

why the equation has up to 2 solution

but it's not a quadratic equation

Can you explain me, please?
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September 4th, 2011, 10:56 AM   #4
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Re: solutions of an equation

Quote:
Originally Posted by versmart
If you mean:





not necessary to put answers to equation and check them instead check the steps that lead you to solve a problem
several times.
I was thinking like you, not necessary to check them
but let's think about it

but for example : abs(x) = x^2 + x - 3
If you don't check them, there are 4 solutions, but if you check, only 2 of them are solution

So, can you or someone else tell me when I should check the solution?

Thank you so much
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September 4th, 2011, 02:17 PM   #5
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Re: solutions of an equation

Quote:
my teacher said the number of solutions of an equation depends on the degree of equation

why the equation has up to 2 solution

but it's not a quadratic equation
Your teacher says this :
"The maximum number of solutions to an equation with degree n is n"
for example could have n solutions or n-m solutions while m<n
special case :
quadratic equation =


0-reform the equation to the form of

1- find

2- if so there are 2 roots
if so there are 2 roots and equal
if there is no real root but complex

Quote:
but for example : abs(x) = x^2 + x - 3
If you don't check them, there are 4 solutions, but if you check, only 2 of them are solution
how you found 4 solutions to that equation?
there are only 2 roots and it's not possible to have more roots:



you should not make another problem for yourself but if you like to check I suggest you this technique:
let be the roots of
always and always:



I use this if I want to check:
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September 4th, 2011, 03:27 PM   #6
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Re: solutions of an equation

Quote:
but it's not a quadratic equation
Then what do you call this?:
Quote:
Originally Posted by daivinhtran
Quote:
not necessary to put answers to equation and check them instead check the steps that lead you to solve a problem
several times.
Yes, but you can still flub up, or perhaps just not know what you're doing, so checking the answers is certainly never a bad idea. So I don't see any "instead" here. It's actually much easier to miss mistakes when you're checking over your work because you tend to see what you think you should, and it's terrifically easy to miss signs and such. In fact, the common mistakes people make can be just the kind of mistake you'd miss (again) when you check it over.

So while it doesn't hurt to check back over your steps, it's also a terrifically good idea to check your answers as well, which I think gives me more comfort that what I did was correct.
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September 5th, 2011, 12:21 AM   #7
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Re: solutions of an equation

Quote:
So while it doesn't hurt to check back over your steps, it's also a terrifically good idea to check your answers as well, which I think gives me more comfort that what I did was correct.
if you pay attention i gave him a simpler method of checking his answers if the equation is second degree:

Quote:
I use this if I want to check:
it is faster than putting 2 answers 2 times into and equation which most of the times need calculator!
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September 5th, 2011, 12:38 AM   #8
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Re: solutions of an equation

Quote:
Originally Posted by versmart
Quote:
it is faster than putting 2 answers 2 times into and equation which most of the times need calculator!
And most of the time I have a calculator. I was simply making a point that there's something to be said for checking answers and that there's certainly nothing wrong with it. Not to mention that I was answering your comment that you should "instead check the steps that led you to solve the problem."
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September 7th, 2011, 03:14 PM   #9
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Re: solutions of an equation

Quote:
Originally Posted by versmart
Quote:

[quote:1fexck7o]but for example : abs(x) = x^2 + x - 3
If you don't check them, there are 4 solutions, but if you check, only 2 of them are solution
how you found 4 solutions to that equation?
there are only 2 roots and it's not possible to have more roots:


[/quote:1fexck7o]

honestly, I have to say you didn't read the question carefully
my question is abs(x) = x^2 + x - 3
it's ABS(x) = |x|

You can't find the correct answer without checking....
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September 7th, 2011, 06:14 PM   #10
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Re: solutions of an equation

Quote:
Originally Posted by daivinhtran
honestly, I have to say you didn't read the question carefully
my question is abs(x) = x^2 + x - 3
it's ABS(x) = |x|

You can't find the correct answer without checking....
Hello daivinhtran,

Your example may not have only two solutions because it is not a polynomial equation. What your teacher said only applies to polynomials.
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