If `a a n d b`are the roots of `x^2-3x+p=0 a n d c , d`are the roots ` – InterviewSolution

InterviewSolution

1.	If `a a n d b`are the roots of `x^2-3x+p=0 a n d c , d`are the roots `x^2-12 x+q=0`where `a , b , c , d`form a G.P. Prove that `(q+p):(q-p)=17 : 15.`
Answer» Let r be the common ratio of the given GP. Then, `b=ar, c=ar^(2)` and `d=ar^(3)`. Also, `a+b=3, ab=p, c+d=12` and `cd=q`. Now, `a+b=3, c+d=12 rArr a(1+r)=3` and `ar^(2) (1+r)=12` `rArr (ar^(2) (1+r))/(a(1+r))=4rArr r^(2) = 4 rArr r=2` `rArr a(1+2)=3rArr a=1`. `:. p=ab=a xx ar=a^(2) r=(1^(2) xx2)=2` and `q=cd=ar^(2) xxar^(3)=a^(2) r^(5)=(1)^(2)xx2^(5)=32`. Hence, `(q+p)/(q-p)=(32+2)/(32-2)=34/30=17/15`.

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