8(a)Root Finding IterationMedium1 markBy sketching a suitable pair of graphs, show that the equation x3=4−2x has exactly one real root.PenEraserUndoRedoClearDraw with the mouse or a finger.Grade answerSolutionGrading criteria
8(b)Root Finding IterationMedium2 marksShow that, if a sequence of real values given by the iterative formulaxn+1=4xn2+23xn3+4converges, then it converges to the root of the equation in 8(a).AnswerTypeWriteMath0 wordsGrade answerSolutionGrading criteria
8(c)Root Finding IterationMedium2 marksShow by calculation that this root lies between 1 and 2.AnswerTypeWriteMath0 wordsGrade answerSolutionGrading criteria
8(d)Root Finding IterationMedium3 marksUse the iterative formula given in 8(b) to calculate this root correct to 2 decimal places. Give the result of each iteration to 5 decimal places.WorkingTypeWriteMath0 wordsGrade answerSolutionGrading criteria