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Question

If a,b,c are distinct rational numbers, then the roots of the quadratic equation (a+b2c)x2+(b+c2a)x+(c+a2b)=0 are


A
rational and distinct
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B
rational and equal 
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C
irrational and distinct
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D
irrational and equal 
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Solution

The correct option is A rational and distinct
(a+b2c)x2+(b+c2a)x+(c+a2b)=0a(x22x+1)+b(x2+x2)c(2x2x1)=0a(x1)2+b[(x1)(x+2)]c[(2x+1)(x1)]=0(x1)[a(x1)+b(x+2)c(2x+1)]=0(x1)[x(a+b2c)(a+c2b)]=0x=1,a+c2ba+b2c
Roots are rational and distinct.
 

Mathematics

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