Using synthetic division method, check whether α = 3 is a root of the polynomial equation:
x4 + x3 - 13x2 - x + 12 = 0
To check whether $\alpha = 3$ is a root of the polynomial $x^4 + x^3 - 13x^2 - x + 12 = 0$ using synthetic division, we first set up the coefficients of the polynomial: $1, 1, -13, -1, 12$. The divisor corresponds to $x - 3$, so we use ______ _______ ____ _______ _________ _______ ____ __________ ___ __________ ____ ___.
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Using Newton-Rapshson method, find an iterative formula to compute the reciprocal of a natural number N.
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i) The equation x3 4x 16 = 0 has a root in the interval [3, 4].
ii) The order of convergence of the secant method is 0.62.
iii) For the system of linear equations:
5x + y + 2z = 34
4y − 3z = 12
10x − 2y + z = −4
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iv) The numerical method:
is relatively stable.
v) The method:
converges to 1.5 for any choice of initial approximation.
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