Solve the Problem $3 \mathrm { x } ^ { 4 } + 2 \mathrm { x } - 4 = 0$

Essay

Solve the problem.
-Use Newton's method to estimate the solutions of the equation $3 \mathrm { x } ^ { 4 } + 2 \mathrm { x } - 4 = 0$ . Start with $\mathrm { x } _ { 1 } = 1$ for the right-hand solution and with $x _ { 0 } = - 1.5$ for the solution on the left. Then, in each case find $x _ { 2 }$ .