f(x)=x3+3x2+4x+4f(x) = x^3 + 3x^2 + 4x + 4f(x)=x3+3x2+4x+4
Show that f(x)f(x)f(x) has a root α \alpha\,α between -2.5 and -1.5
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=−(4x+4x2+3)\displaystyle x = -\left(\frac{4x+4}{x^2} + 3\right)x=−(x24x+4+3)
Use the iteration formula xn+1=−(4xn+4xn2+3)\displaystyle x_{n+1} = -\left(\frac{4x_n+4}{x_n^2} + 3\right)xn+1=−(xn24xn+4+3) with x0=−2.5x_0 = -2.5x0=−2.5 to find, to 3 decimal places, the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
By choosing a suitable interval, prove that α=−2.000\alpha = -2.000α=−2.000 to 3 decimal places
329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.