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

Since p(x) = 0 has purely imaginary roots,          p(x) = ax2 + c, where a and c have same sign.Also, p(p(x)) = 0⇒p(x) is purely imaginary⇒ax2 + c is purely imaginaryHence, x cannot be either purely real or purely imaginary.