TS EAMCET 7 May 2018 Shift 1 Solved Paper

Given: The roots of the equation are α,β.
The equation is x2+5x+2=0
x2+5x+2=0
α2+5α+2=0
5α+2=−α2
Similarly,
5β+2=−β2
The sum of the roots is,
α+β=−5
The multiple of the roots is,
αβ=2
The equation is,
(

α

2+5α

)2+(

β

2+5β

)2 =(

α

−α2

)2+(

β

−β2

)2
=

α2+β2

(αβ)2

=

(α+β)2−2αβ

(αβ)2

=

25−4

4

=

21

4