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[Post New] 17 Oct 2009 14:36:55 IST
   Subject: quadratic equations
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VARUN (aryan) (20)

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if the equations x2+bx+ca=0 and x2+cx+ab=0  (where b is not equal to c) have one root  common ,then show that a+b+c=0 .
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[Post New] 17 Oct 2009 16:00:30 IST
   Subject: quadratic equations
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Srujana (2785)

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Let p be the comon root ,then

 

f(p)=g(p)=0

 

Rightarrow p^2+pb+ca=0

      p^2+pc+ab=0

 

Solving both,

 

p(b-c)=a(b-c)

 

Hence 'a' is the common root

 

Rightarrow a^2+ab+ca=0

 

Rightarrow a=0 or a+b+c=0

 
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