IGNOU BMTE 144 2026 - The roots of the quadratic equation are given by &nbsp

Question

The roots of the quadratic equation $x^2 + ax + b = 0$ are given by $\alpha$ and $\beta$ . Show that the iteration $x_{k+1} = \frac{-(ax_k + b)}{x_k}$ will converge near $x = \alpha$ when $|\alpha| > |\beta|$ .

09 Jan 2026

Answer :

Word Count : 159

Consider the quadratic equation: [ x^2 + ax + b = 0 ] with roots (\alpha) and (\beta), where (|\alpha| > |\beta|). The iteration formula is: [ x_{k+1} = -\frac{ax_k + b}{x_k}. ] We can write this as a function: [ f(x) = -\frac{ax + b}{x} = -a -

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