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 $(1)$ ]

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

$=-1/2$

If alpha,beta are the roots of 2x^2+x+3=02x^2+x+3=0 then (1-alpha)/(1+alpha)+(1-beta)/(1+beta)(1-alpha)/(1+alpha)+(1-beta)/(1+beta) is?