Solution:
Solution
Let α , β Î R If α , β2 be the roots .......
For the equation x2 – px + 1 = 0,
the product of roots, αβ2 = 1
and for the equation x2 – qx + 8 = 0,
the product of roots α2β = 8 = > αβ= 2
From αβ2 = 1, we have β= 1/2 and from
α2β = 8, we have α= 4
Hence, from sum of roots = -b /a " relation,
we have p = α + β2 = 4 + 1/4 = 17/4
and q = α2 + β = 16 + 1/2 = 33/ 2
? r /8 is arithmetic mean of p and q
r /8 = (p+q )/2 = > 4(p+q) = 83
