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
- AOnly purely imaginary roots
- BAll real roots
- CTwo real and two purely imaginary roots
- 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