Name: Date:

Question 1: a) Show that the equation x^2-9x+19=0 can be arranged to give x=- {\Large \frac{19}{x-9}} b) Starting with x_0=3 use the iterative formula x_{n+1} =- {\Large \frac{19}{x_n -9}} to obtain a solution of the equation x^2-9x+19=0 correct to 2 decimal places |

Question 2: a) Show that the equation x^2-25x+1=0 can be arranged to give x= \sqrt{25x-1} b) Starting with x_0=25 use the iterative formula x_{n+1} = \sqrt{25x_n -1} to obtain a solution of the equation x^2-25x+1=0 correct to 2 decimal places |

Question 3: a) Show that the equation x^2-21x+11=0 can be arranged to give x= {\Large \frac{x^2+11}{21}} b) Starting with x_0=1 use the iterative formula x_{n+1} = {\Large \frac{x_n^2+11}{21}} to obtain a solution of the equation x^2-21x+11=0 correct to 2 decimal places |

Question 4: a) Show that the equation x^2-29x+7=0 can be arranged to give x=- {\Large \frac{7}{x-29}} b) Starting with x_0=0 use the iterative formula x_{n+1} =- {\Large \frac{7}{x_n -29}} to obtain a solution of the equation x^2-29x+7=0 correct to 2 decimal places |

Question 5: a) Show that the equation x^2-23x+3=0 can be arranged to give x= \sqrt{23x-3} b) Starting with x_0=23 use the iterative formula x_{n+1} = \sqrt{23x_n -3} to obtain a solution of the equation x^2-23x+3=0 correct to 2 decimal places |

© GCSEMathsWorksheets.com |

Show Answers
Hide Answers

© GCSEMathsWorksheets.com

# Answers

Question 1: a) x^2-9x+19=0 \implies x^2-9x=-19 \implies x(x-9)=-19 \implies x=- {\Large \frac{19}{x-9}} b) Root to 2 decimal places = 3.38 |

Question 2: a) x^2-25x+1=0 \implies x^2 =25x -1 \implies x= \sqrt{25x-1} b) Root to 2 decimal places = 24.96 |

Question 3: a) x^2-21x+11=0 \implies x^2+11 =21x \implies x= {\Large \frac {x^2+11}{21}} b) Root to 2 decimal places = 0.54 |

Question 4: a) x^2-29x+7=0 \implies x^2-29x=-7 \implies x(x-29)=-7 \implies x=- {\Large \frac{7}{x-29}} b) Root to 2 decimal places = 0.24 |

Question 5: a) x^2-23x+3=0 \implies x^2 =23x -3 \implies x= \sqrt{23x-3} b) Root to 2 decimal places = 22.87 |

© GCSEMathsWorksheets.com