Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The root of x4 – 2x3 + 3x2 – 8 = 0 in the interval [1, 2]

Use Newton's method to approximate a root of the equation 3x³ + 6x + 2 = 0 as follows. Let x₁ = -2 be the initial approximation. The second approximation 2 is and the third approximation 3 is (Although these are approximations of the root, enter exact expressions for each approximation.)

Use Newton's method to approximate a root of the equation 2x +6z+ 430 as follows. Let 1 2 be the initial approximation. The second approximation T2 is and the third approximation 23 is (Although these are approximations of the root, enter exact expressions for each approximation.)

Use Newton's method to approximate a root of the equation 5x³ + 6x + 4 = 0 as follows. Let x1 = - 1 be the initial approximation. The second approximation x2 is and the third approximation x3 is (Although these are approximations of the root, enter exact expressions for each approximation.)