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Solution


Q.

(x² + 1)² − x² = 0 has
1 Four real roots  
2 Two real roots  
3 No real roots  
4 One real root  

Ans.

(3)

Given equation: (x² + 1)² − x² = 0 ⇒ (x² + 1 − x)(x² + 1 + x) = 0.

⇒ (x² − x + 1)(x² + x + 1) = 0      or    x² − x + 1 = 0,
Its  discriminant D = (−1)² − 4×1×1 = −3 < 0
Its  discriminant D = 1² − 4×1×1 = −3 < 0

So, there are no real roots.