Question

Use MuPAD to solve the polynomial equation x³ + 8x² + ax + 10 = 0 for x in terms of the parameter a, and evaluate your solution for the case a = 17. Use MuPAD to check the answer.

Answer 1

The polynomial equation given to us is

x3 = 8x2 + ax + 10 = 0

 

It is required to solve the above equation for x in terms of a. This can be done in MATLAB using the command solve. Then solution for the case a = 17 is required.

 

The MATLAB code is given below. The check part is done by calculating the polynomial again using the roots. This can be done using the MATLAB command poly(A) where A is the roots of the polynomial.

 

Input:

syms x a

eq = x^3 + 8*x^2 + a*x + 10;

sol = solve(eq)

% substituting the value of a = 17

roots = subs(sol, a, 17);

roots = double(roots)

% checking in MATLAB

poly(roots)

 

Output:

Sol =

root(z^3 + 8*z^2 + a*z + 10, z, 1)

root(z^3 + 8*z^2 + a*z + 10, z, 2)

root(z^3 + 8*z^2 + a*z + 10, z, 3)

roots =

-5

-2

-1

ans =

          1      8        17        10

 

The roots of equation for a = 17 is

roots = -5, -2, -1.

The polynomial from the roots is made in MATLAB using the command poly. The polynomial equation thus obtained is same as given. 

Hence, our answer is verified.

The polynomial from the roots is made in MATLAB using the command poly. The polynomial equation thus obtained is same as given. 

Hence, our answer is verified.