Use Newton’s method to estimate the solution of the equation 6x^{2}+x-1=0. Start with x_{0} = -1 for the left solution and x_{0} = 1 for the right solution. Find x_{2} in each case.

Using Newton’s method with x_{0} = -1, the third approximation, x_{2}, to the left solution to 6x^{2 }+ x – 1 = 0 is …….?.

Using Newton’s method with x_{0}=1, the third approximation, x_{2}, to the right solution to 6x^{2 }+ x – 1 = 0 is ……?

**Solution:-**

Using Newton’s method with x_{0} = -1, the third approximation, x_{2}, to the left solution to 6x^{2 }+ x – 1 = 0 is** -0.5168.**

Using Newton’s method with x_{0}=1, the third approximation, x_{2}, to the right solution to 6x^{2 }+ x – 1 = 0 is **0.3672.**