f(x)=x3+3x2+x+1f(x) = x^3 + 3x^2 + x + 1f(x)=x3+3x2+x+1
Show that f(x)f(x)f(x) has a root between -3 and -2.5
Show that the equation x=−(x+1x2+3)\displaystyle x = -\left(\frac{x+1}{x^2} + 3\right)x=−(x2x+1+3) can be written in the form f(x)=0f(x) = 0f(x)=0
Use the iteration formula xn+1=−(xn+1xn2+3)\displaystyle x_{n+1} = -\left(\frac{x_n+1}{x_n^2} + 3\right)xn+1=−(xn2xn+1+3) 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=−2.769\alpha = -2.769α=−2.769 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.