Question

4. Check, whether the equation (x²+1)²-x²= 0 has real roots or not?​

Answer 1

Answer:

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.