Problem 848

Use Newton’s method to estimate the solution of the equation 6x²+x-1=0. Start with x₀ = -1 for the left solution and x₀ = 1 for the right solution. Find x₂ in each case.

Using Newton’s method with x₀ = -1, the third approximation, x₂, to the left solution to 6x² + x – 1 = 0 is …….?.

Using Newton’s method with x₀=1, the   third approximation, x₂, to the right solution to 6x² + x – 1 = 0 is ……?

 

Solution:-

 

Using Newton’s method with x₀ = -1, the third approximation, x₂, to the left solution to 6x² + x – 1 = 0 is -0.5168.

Using Newton’s method with x₀=1, the   third approximation, x₂, to the right solution to 6x² + x – 1 = 0 is 0.3672.