AP EAPCET 19-Aug-2021 Shift 2 Paper

∵p,q,r,s are in AP.
Let p=a,q=a+d,r=a+2d,s=a+3d
Given, p.q are roots of
x2−2x+A=0
Then, p+q=2 and pq=A
⇒2a+d=2 ...(i)
Also, r and s are roots of x2−18x+B=0
Then,r+s=18‌and‌r‌s=B
⇒2a+5d=18 ...(ii)
Solving Eqs. (i) and (ii), we get
a=−1,d=4
Now, pq=A ‌‌‌‌‌‌‌‌‌‌‌ (product of roots)
OrA=a(a+d)=(−1)(−1+4)
A=−3
andrs=B
or B=(a+2d)(a+3d)1=(−1+8)(−1+12)=77
∴A=−3,B=77