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  • If r be the ratio of the roots of the equation ax^2+bx+c=0 show that (r+1)^2 / r = b^2 / ac

If r be the ratio of the roots of the equation ax^2+bx+c=0 show that (r+1)^2 / r = b^2 / ac

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Solution:   Given equation is    ax^2+bx+c=0 hspace1cm............(1)

     Let   the roots of equation   (1)  be  alpha  and  r alpha then 

      \ \ Rightarrow hspace1cm alpha+ralpha =-fracbahspace1cm.........(2)\ \ Rightarrow hspace1cmralpha^2=fraccahspace1cm..........(3)\ \ Rightarrow hspace1cmalpha=-fracba(r+1)

Putting  the value of   alpha in (3)  , we get 

   \ \ Rightarrow hspace1cmfracrb^2a^2(r+1)^2=fraccaRightarrow fracb^2ac=frac(r+1)^2r                  

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Deependra Verma

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