f(x)=x3+2x2+2x+3f(x)=x^3+2x^2+2x+3f(x)=x3+2x2+2x+3
Show that f(x)f(x)f(x) has a root α \alpha\,α between -1.5 and -2
Show that the equation f(x)=0f(x)=0f(x)=0 can be written in the form x=−(2x+3x2+2)\displaystyle x=-\left(\frac{2x+3}{x^2}+2\right)x=−(x22x+3+2)
Use the iteration formula xn+1=−(2xn+3xn2+2)\displaystyle x_{n+1}=-\left(\frac{2x_n+3}{x_n^2}+2\right)xn+1=−(xn22xn+3+2) with x0=−2x_0=-2x0=−2 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=−1.811\alpha=-1.811α=−1.811 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.