The roots of the quadratic equation are given by

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 + ____ ______ __________ _________ ___ _________ _____ ________ ____ __________ _____ _______.
________ _______ _________ ____ _________ _________ ___ ____ _______ ___.
_________ ____ __________ _______ ____ _____ ___ _____ ___ ________ ___ _____.
________ ____ _______ _________ ___ _____ _____ ______ _____.
__________ _________ ____ ______ ____ ___ _________ _____.
_______ ___ _______ __________ ___ ______ ________ ____ ____ ___ ____.
_____ _______ _____ ___ ___ ____ ______ __________ _____ _______.
________ ___ _________ _____ _____ ________ __________ _____ ______ ____ __________ ___.
________ ______ ____ __________ ________ ________ __________ ________.
__________ _______ _____ ____ ____ __________.
_____ __________ _________ ______ ______ ____ _________ ____ ___.
______ _____ _____ _______ ______ _______ _______ _____ ___ _________.
_____ ___ _______ ______ _____ ______ _________ ___ _________ ____ _______.
Get Full Answer on WhatsApp

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers

IGNOU NEWS

Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★