1 Using Matlab find all real and complex roots of the follow

1) Using Matlab, find all real and complex roots of the following polynomial equation:

(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)=8

2) Using Matlab, find the root for the following system of equations. Both x and y are positive.

a: (x^2)cos(y)=1

b: e^(-4x)+1

Solution

1.

function y = f(x)

y = (x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7) - 8;

%Find the zero of f(x) near 0.

fun = @f; % function

x0 = 0; % initial point

z = fzero(fun,x0)

OR

roots(p)

where p is a vector containing value of coefficient of x⁷,x⁶......constant term.

2. a)

syms x y

eqn = (x^2)cos(y) == 1;

solx = solve(eqn,x)

soly = solve(eqn,y)

b) no root exists for this equation you can try it with fzero