Using synthetic division method, check whether α = 3 is a root of the polynomial equation:
x4 + x3 - 13x2 - x + 12 = 0
To determine whether α = 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 in descending powers of x: 1 _______ _________ _________ ______ ___ ____ _______ _______ ________ _______.
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) Use the Euler’s method to solve numerically the initial value problem:
with h = 2.0 on the interval [0, 1].
Find the first term of the series whose second and subsequent terms are ,0,3,8 − 0,1 using difference table.
From the following data, calculate the population in the year 1985:
| Year | Population (in , 000) |
| 1971 | 12 |
| 1981 | 15 |
| 1991 | 20 |
| 2001 | 27 |
| 2011 | 49 |
Which of the following statements are true and which are false? Give a short proof or a counterexample in support of your answer:
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
the matrix is diagonally dominant.
iv) The numerical method:
is relatively stable.
v) The method:
converges to 1.5 for any choice of initial approximation.
Using Newton-Rapshson method, find an iterative formula to compute the reciprocal of a natural number N.
Solve the system of equations:
x + 2y + z = 3
3x − 2y − z4 = −2
2x + 3y − z = −6
using Gauss-Elimination method.
Given the data:
f(3) = 168,
f(7) = 120
and f(9) = 72
If f(k) is estimated as 138 using the Newton’s form of the interpolating polynomial, then find the value of .k