Question

Need these done on matlab

4. (10%) Given the roots (.--2, x-3.x-8), reconstruct the corresponding polynomial 5. (10%) Add the following polynomials: f(x)- x3-x +3 g(x) x2-8 h(x)-x*+2 6. (10%) Multiply the polynomials from Problem 5.

Answer 1

4.CODE:

clear all;close all;clc;
r=[-2,3,8];
x= sym('x');
poly_eqn=expand(prod(x-r))

OUTPUT:

poly_eqn =

x^3 - 9*x^2 + 2*x + 48

5. CODE:

clear all;close all;clc;
% write equations as standard matlab vectors...
%adjust their coefficient arrays putting zeros for absent powers, so that
% coefficients of terms with the same power will be on the same positions within both coefficient arrays.
eq1=[0 1 0 -1 3];
eq2=[0 0 1 0 -8];
eq3=[1 0 0 0 2];
added_coeff=eq1+eq2+eq3;
%to get back the equation from coefficient....
added_eq = poly2sym(added_coeff)

OUTPUT:

added_eq =

x^4 + x^3 + x^2 - x - 3

6. CODE:

clear all;close all;clc;
eq1=[0 1 0 -1 3];
eq2=[0 0 1 0 -8];
eq3=[1 0 0 0 2];
r1=conv(eq1,eq2);
prod_coeff=conv(r1,eq3);
multiplied_eq = poly2sym(prod_coeff)

OUTPUT:

multiplied_eq =

x^9 - 9*x^7 + 3*x^6 + 10*x^5 - 24*x^4 - 18*x^3 + 6*x^2 + 16*x - 48