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KVPY2018MathematicsQuadratic Equation

The number of real roots of the polynomial equation x 4 - x 2 + 2 x - 1 = 0 is

Options

  1. A0
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

Given, 4 - x 2 + 2 x - 1 = 0 ⇒    x 4 - ( x - 1 ) 2 = 0 ⇒ x 2 - x + 1 x 2 + x - 1 = 0 ⇒ x 2 - x + 1 = 0 or x 2 + x - 1 = 0 ⇒ x 2 - x + 1 = 0 has no real roots. ⇒ x 2 + x - 1 = 0 has two real roots

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