f(x)=x3+4x2+2x+1f(x) = x^3 + 4x^2 + 2x + 1f(x)=x3+4x2+2x+1
Show that f(x)f(x)f(x) has a root between -3.5 and -4
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=−(2x+1x2+4)\displaystyle x = -\left(\frac{2x+1}{x^2} + 4\right)x=−(x22x+1+4)
Use the iteration formula xn+1=−(2xn+1xn2+4)\displaystyle x_{n+1} = -\left(\frac{2x_n+1}{x_n^2} + 4\right)xn+1=−(xn22xn+1+4) with x0=−4x_0 = -4x0=−4 to find, to 3 decimal places, the values of x1,x2 x_1, x_2\,x1,x2 and x3x_3x3.
The root of f(x)=0f(x) = 0f(x)=0 is α\alphaα. By choosing a suitable interval, prove that α=−3.512\alpha = -3.512α=−3.512 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.