f(x)=x3+4x2+3x+1f(x) = x^3 + 4x^2 + 3x + 1f(x)=x3+4x2+3x+1
Show that f(x)f(x)f(x) has a root between -3.5 and -3
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=−(3x+1x2+4)\displaystyle x = -\left(\frac{3x+1}{x^2} + 4\right)x=−(x23x+1+4)
Use the iteration formula xn+1=−(3xn+1xn2+4)\displaystyle x_{n+1} = -\left(\frac{3x_n+1}{x_n^2} + 4\right)xn+1=−(xn23xn+1+4) with x0=−3x_0 = -3x0=−3 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=−3.148\alpha = -3.148α=−3.148 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.