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EAMCET Engineering 2009 Solved Paper

Section: Mathematics

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Question : 91 of 160

Marks: +1, -0

The

(x-a)(x-a-1)+(x-a-1)(x-a-2)

+(x-a)(x-a-2)=0, a \in R

equal
imaginary
real and distinct
rational and equal

Solution:

Given,

(x-a)(x-a-1)+(x-a-1)(x-a-2)

+(x-a)(x-a-2)=0

Let

x-a=t

, then

\;t(t-1)+(t-1)(t-2)+t(t-2)=0

\Rightarrow t^2-t+t^2-3 t+2+t^2-2 t=0

\Rightarrow 3 t^2-6 t+2=0

\Rightarrow t=\;\frac{6 \pm \sqrt{36-24}}{2(3)}=\;\frac{6 \pm 2\sqrt{3}}{2(3)}

\Rightarrow x-a=\;\frac{3 \pm \sqrt{3}}{3}

\Rightarrow x=a+\;\frac{3 \pm \sqrt{3}}{3}

Hence,

x

is real and distinct.

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