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August 3rd, 2013, 07:57 PM  #1 
Member Joined: Jul 2013 Posts: 58 Thanks: 0  Binomial as a,b and c in a quadratic equation.
the question : Show the roots of the equation are always real and they can not be equal unless a=b=c. a= (xa)(xb) , b=(xb)(xc) , c = (xc)(xa). (xa)(xb) = x^2bxax+ab. ......... I ended up with this I tried to solve this with quadratic formula but I could not do it. Each binomial turned out be a quadratic equation.. i missed some method to factor out this equation.. please help. 
August 3rd, 2013, 09:03 PM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Binomial as a,b and c in a quadratic equation. Quote:
 
August 3rd, 2013, 09:05 PM  #3  
Senior Member Joined: Apr 2013 Posts: 425 Thanks: 24  Re: Binomial as a,b and c in a quadratic equation. Quote:
Thank You!  
August 3rd, 2013, 09:19 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,933 Thanks: 2207 
One needs to know that a, b and c are real. (xa)(xb) + (xb)(xc) + (xc)(xa) = 3x²  2(a + b + c)x + ab + bc + ca = 0. Discriminant = 4(a + b + c)²  12(ab + bc + ca) = 2((a  b)² + (b  c)² + (c  a)²), etc. 
August 4th, 2013, 11:47 AM  #5  
Member Joined: Jul 2013 Posts: 58 Thanks: 0  Re: Binomial as a,b and c in a quadratic equation. Quote:
 
August 4th, 2013, 11:49 AM  #6  
Member Joined: Jul 2013 Posts: 58 Thanks: 0  Re: Quote:
 
August 4th, 2013, 12:14 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,933 Thanks: 2207 
You have to put the original quadratic expression into a form that allows you to find its discriminant easily. The discriminant can then be arranged to make it easy to see that it cannot be negative, and under what circumstances it can be zero.

August 8th, 2013, 07:45 PM  #8  
Member Joined: Jul 2013 Posts: 58 Thanks: 0  Re: Quote:
I am getting the above equation .. where am I mistaking ?  
August 8th, 2013, 07:53 PM  #9 
Senior Member Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11  Re: Binomial as a,b and c in a quadratic equation. can be written as 
August 9th, 2013, 03:20 AM  #10 
Member Joined: Jul 2013 Posts: 58 Thanks: 0  Re: Binomial as a,b and c in a quadratic equation.
thanks 

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binomial, equation, quadratic 
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