7. The equation x² + ax + b = 0, has two real roots a and B. Show that the iteration method (i) Xk-1 = - (axx + b)/x£, is convergent near x = a, if | a |> |BI (ii) Xk-1 =- b/(X +a), is convergent near x = a, if | a|

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7. The equation x² + ax + b = 0, has two real roots a and ß. Show that the iteration
method
(i) xk+1 = - (axk + b)/xk, is convergent near x = a, if | a |>Iß |,
(ii) Xk÷1 = - b/(Xk + a), is convergent near x = a, if | a |<|B |.
Transcribed Image Text:7. The equation x² + ax + b = 0, has two real roots a and ß. Show that the iteration method (i) xk+1 = - (axk + b)/xk, is convergent near x = a, if | a |>Iß |, (ii) Xk÷1 = - b/(Xk + a), is convergent near x = a, if | a |<|B |.
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