If alpha,beta are the roots of #2x^2+x+3=0# then #(1-alpha)/(1+alpha)+(1-beta)/(1+beta)# is?

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Answer 1 · 2018-04-30T19:37:46

#-1/2#

We know that,

If #alpha and beta# are the roots of #ax^2+bx+c=0 ,# then

#alpha+beta=-b/a and alpha*beta=c/a#

Here,

#2x^2+x+3=0=>a=2 ,b=1and c=3#

So,

#color(red)(alpha+beta=-1/2 and alpha*beta=3/2...to(1)#

Given,

#(1-alpha)/(1+alpha)+(1-beta)/(1+beta)=(1-alpha+beta- alphabeta+1+alpha-beta-alphabeta)/(1+alpha+beta+alphabeta)#

#=(2-2alphabeta)/(1+(alpha+beta)+alphabeta)#

#=(2-2(3/2))/(1-1/2+3/2)...to#[ from#(1)# ]

#=(2-3)/(1+1)#

#=-1/2#