Correct Answer: A
Explanation:
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.