Let p and q be roots of the equations x2 – 2x + A = 0 and let r and s be the roots of the equation x2 – 18 + B = 0. If p < q < r < s are in arithmetic progression the A = ………….. and B = …………

The answer is A=10 , B=63 

 here let p=a,q=a+r,r=a+2r,s=a+3r;

 then here p+q=2            =>2a+r=2

         also r+s=18           =>2a+5r=18

 solving we get r=4,a=-1;

p=-1, q=3, r=7, s=11

A=pq= -3, B=rs = 77;

I USE PUT & CHECK FORMULA IN THIS QUESTION.

P + Q = 2 , PQ=A ..............(1)

R + S = 18 , RS = B ...............(2)

-1,3,7,11 ARE IN A.P. SATISFYING THE RELATIONS (1) & (2)

SO , P=-1, Q=3 , R=7, S=11

SO, PQ= -3 = A

      RS= 77 = B