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JEE Advanced2014MathematicsQuadratic EquationActual

The quadratic equation p ( x ) = 0 with real coefficients has purely imaginary roots. Then the equation p ( p ( x ) ) = 0 has

Options

  1. AOnly purely imaginary roots
  2. BAll real roots
  3. CTwo real and two purely imaginary roots
  4. DNeither real nor purely imaginary roots

Correct answer

D. Neither real nor purely imaginary roots

Step-by-step solution

P x = a x 2 + b with a, b of same sign. P P x = a a x 2 + b 2 + b If x ϵ R o r i x ϵ R ⇒ x 2 ϵ R ⇒ P x ϵ R ⇒ P P x ≠ 0 Hence real or purely imaginary number can not satisfy P P x = 0

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