1.

(x2 + 1)2 - x2 = 0 hasA. four real rootsB. two real rootsC. no real roots D. one real root.

Answer»

C. no real roots

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.


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