Question 6627
  {{{ f(x) = 2x^3 - 4x^2 + 8x - 3 }}} is a polynomial of third degree (odd)
 in real coefficients.
 Hence   {{{ f(x) = 2x^3 - 4x^2 + 8x - 3 }}} = 0 must have one real 
 or three real roots.

 When it has only one real root, the other two are complex conjugate
 number.
 Hence, the possible number of imaginary zeros is 2 or 0.
 [In fact, the complex roots appear always in pairs]

 In fact, f(0) = -3 < 0 and f(1) = 3 > 0,so there is a zero of f
 between 0 and 1. Also,  since f'(x) = 6x^2 -8x + 8 = 2(3x^2 -4x + 4) =0
 has no real roots, so f has only one real zero and two complex zeros.


 Kenny