The given quadratic equation is x² – 2px + 1 = 0.

And, Discriminant D of the quadratic equation ax² + bx + c = 0 is given by –

D = b² – 4ac

Comparing the equation ax² + bx + c = 0 with given quadratic equation is x² – 2px + 1 = 0, we get –

a = 1, b = – 2p and, c = 1

∴ D = (– 2p)² – 4(1)(1) = 4p² – 4 = 4(p² – 1)

For no real roots,

D < 0

⇒ 4(p² – 1) < 0

⇒ p² – 1 < 0

⇒ (p + 1)(p – 1) < 0

∴ p ∈ (– 1,1)

Thus, p can take any values between – 1 and 1 for no real roots of given quadratic equation.