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September 4th, 2011, 10:14 AM  #1 
Senior Member Joined: Mar 2011 Posts: 105 Thanks: 0  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 
September 4th, 2011, 10:30 AM  #2 
Senior Member Joined: Jul 2010 Posts: 103 Thanks: 0  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. 
September 4th, 2011, 10:45 AM  #3  
Senior Member Joined: Mar 2011 Posts: 105 Thanks: 0  Re: solutions of an equation Quote:
why the equation has up to 2 solution but it's not a quadratic equation Can you explain me, please?  
September 4th, 2011, 10:56 AM  #4  
Senior Member Joined: Mar 2011 Posts: 105 Thanks: 0  Re: solutions of an equation Quote:
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  
September 4th, 2011, 02:17 PM  #5  
Senior Member Joined: Jul 2010 Posts: 103 Thanks: 0  Re: solutions of an equation Quote:
"The maximum number of solutions to an equation with degree n is n" for example could have n solutions or nm solutions while m<n special case : quadratic equation = 0reform 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:
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:  
September 4th, 2011, 03:27 PM  #6  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: solutions of an equation Quote:
Quote:
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.  
September 5th, 2011, 12:21 AM  #7  
Senior Member Joined: Jul 2010 Posts: 103 Thanks: 0  Re: solutions of an equation Quote:
Quote:
 
September 5th, 2011, 12:38 AM  #8  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: solutions of an equation Quote:
 
September 7th, 2011, 03:14 PM  #9  
Senior Member Joined: Mar 2011 Posts: 105 Thanks: 0  Re: solutions of an equation Quote:
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....  
September 7th, 2011, 06:14 PM  #10  
Senior Member Joined: Apr 2011 From: Recife, BR Posts: 352 Thanks: 0  Re: solutions of an equation Quote:
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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