TS EAMCET 11-Sep-2020 Shift 2 Solved Paper

Given n1,n2,n3 are roots of the equation
E1:x3+x2+lx+n=0....(i)
∴ Sum of roots x1+x2+x3=−1.....(ii)
Now, E2:x3+ax2+bx+c=0 is reciprocal equation of class one ⇒c=1 and a=b
∴‌‌E2:x3+ax2+ax+1=0....(iii)
Given, Eq. (iii) have roots
‌

x1−1

2

,‌

x2−1

2

,‌

x3−1

2

⇒‌‌‌

x1−1

2

+‌

x2−1

2

+‌

x3−1

2

=−a
⇒‌‌‌

x1+x2+x3

2

−‌

3

2

=−a
From Eq. (ii),
x1+x2+x3=−1
‌

−1

2

−‌

3

2

=−a⇒a=2
∴ Eq. (iii), x3+2x2+2x+1=0
⇒‌‌x=‌

−1±√3i

2

∴ Given, ‌

x1−1

2

=−1⇒x1=−1
‌

x2−1

2

=‌

−1+√3i

2

⇒x2=√3i
∴ Roots of these two equation excluding common roots are