(x2 + 1)2 - x2 = 0 has
Let’s simplify the equation,
(x2 + 1)2 - x2 = 0
⇒ x4 + 2x2 + 1 - x2 = 0
⇒ x4 + x2 + 1 = 0
Let x2 = y,
⇒ y2 + y + 1 = 0
D = b2 - 4ac = 0
= 12 - 4(1)(1)
∴ D = -3 < 0
Hence, the equation (x2 + 1)2 - x2 = 0 has no real roots.