Solution: The equation has no real root, which is proved as follows:

Prove:

By (2p+ 1)/(p+2) < 0 gives -2.

Discriminant δ = 4-4 (5-p 2) = 4 (p 2-4)

∵-2 & lt； p & lt- 1/2

∴ 1/4<； p^2<； four

∴δ=4(p^2-4)<； 0

∴ x 2-2x+5-p 2 = 0 has no real root.