Answer :
[tex]3x^3-2x^2+5x - 6 = 0\ \ \ \ \ - equation\ 1\\ \\ As\ odd\ terms\ add\ up\ to\ even\ terms\ (coefficients), x = 1\ is\ a\ root. \\ \\ (x-1)(3x^2+ax+6) = 0\\ \\ coefficient\ of\ x^2\ term\ is = -3+a = -2\ \ in\ equation\ 1. \\ \\ So,\ \ a = 1\\ \\ Check\ coefficient\ of\ x^1\ term: \\. \ \ \ \ \ -a+6 = -1+6 = 5,\ \ \ matches\ equation 1 \\ \\3x^2+x+6 = 0 \\ \\x = \frac{-1+-\sqrt{1-72}}{6}\\ \\ Roots\ are :\\ \\ x = 1 (real),\ Imaginary:\ \frac{-1+\sqrt{71}j}{6}, \ and\ \frac{-1-\sqrt{71}j}{6}.[/tex]