Find the positive value of k, for which the equation x2 + kx + 64 =0 and x2 - 8x + k=0 will both have real roots.
if the equaion x2+kx+64=0 has real roots, then D>=0
k2-256>=0 => k2>=256 => k2>=(16)2 => k>=16.- (1)
if the equation x2-8x+k=0 has real roots.
then D>=0 => 64-4k>=0 => 4k<=64 => k<=16 - (2)
from (1) and (2) we get k=16