2014/064) Find the sum of the cubes of the roots of cubic 3x^3-2x+4=0?

if a,b c are roots then
a+b+ c = 0 ... (1) (coefficient of $x^2$)

$3a^3 = 2a - 4 \cdots  (2)$
$3b^3 = 2b - 4 \cdots  (3)$
$3c^3 = 2c- 4 \cdots (4)$
add to get
$3(a^3+b^3+c^3) = 2 (a+b+c) - 12 = -12$ ( from (1))
or
$a^3+b^3 + c^3 = - 4$