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 ________ ______ _________ __________ _________ ____ ________ _________ __________ ____.
__________ __________ _________ _________ ________ _______ ___ ____ ___ _________ _________.
________ _______ _________ _________ _________ ______ ________ ________ __________ _____.
_____ __________ ______ _____ ___ ____ ________ _____ ______ _____.
__________ ______ ________ _______ ____ __________ ____ _________ _______ ________.
___ ______ ___ ________ ____ _________ _______ ____ _______ ______ __________ _____.
______ _________ _____ _____ _______ _______ _________.
_________ __________ _______ __________ ___.
______ _________ __________ _________ _________.
_____ ___ ______ ____ ________ __________ _________ _____ ______ ______ _________.
________ ____ ______ ________ _____.
_________ ________ ____ ____ ___ ______.
_________ ___ _______ _______ ________ ____ _____ ________.
_______ ________ ______ __________ _____ _________.
__________ ___ ______ _________ ________.
____ ______ __________ ___ ________ ________ _____ ___ _______ ____ _____ __________.
___ __________ ______ ____ ________ _________ _______ _______ __________ _______.
__________ __________ _________ ________ ___ ______ _______ ________ _____ ________ ________.
______ ____ ________ ___ ________ ___.
_________ ____ _________ ____ _________ ______ _____ _____.
________ ______ ___ ______ _____ _________ ___.
________ ________ _________ __________ ___ _____ ____ _____ _____.
______ ____ ______ _______ ______ _______ __________ __________ __________ _______ ____ __________.
______ ___ ________ __________ __________ _________ _________ _______ __________.
____ ____.
Get Full Answer on WhatsApp
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.
) Use the Euler’s method to solve numerically the initial value problem:
with h = 2.0 on the interval [0, 1].
Use secant method to determine the root of the equation cos x - xex = 0. Take the initial approximation as x0 = 0, x1 = 1 and perform two iterations of the method.
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 |
Estimate the eigen values of the matrix:
using the Gerschgorin bounds. Also, draw the rough sketch of the region in which the eigen values lie.
Calculate the nth divided difference of 1/x, on the nodal points X0 , X1 , ......., Xn .
Using synthetic division method, check whether α = 3 is a root of the polynomial equation:
x4 + x3 - 13x2 - x + 12 = 0