Question

Consider the following polynomial

?(?)=(?+2)(?−10)(?+4)(?−2)

a)Use Matlab to multiply these terms in order to form a 4thorder polynomial

b)Apply the ‘roots’ function to your answer in part a to verify your calculation was correct.

c)Use Matlab to divide your polynomial answer in part aby the term (s+2

)d)Apply ‘roots’ to your answer in part c to verify your calculation was correct.

Answer 1

a)

syms s

d=s-2;

c=s+2;

b=s+4;

a=s-10;

p= expand(a*b*c*d)

disp("This is the 4th order function")

Output -

p =

s^4 - 6*s^3 - 44*s^2 + 24*s + 160

b)

P=[1 -6 -44 24 160];

disp("The roots are")

r=roots(P)

Output -

The roots are

r =

10.0000
2.0000
-4.0000
-2.0000

c)

syms s

p=(s^4)-6*(s^3)-44*(s^2)+24*s+160;

d=(s+2);

vars=[s];

[r,q]= polynomialReduce(p,d,vars)

disp("This is the reduced polynomial")

Output -

r =

0


q =

s^3 - 8*s^2 - 28*s + 80

This is the reduced polynomial

Here denotes the remainder and q the quotient that is the reduced polynomial.

d)

q=[1 -8 -28 80]

R=roots(q)

disp("Hence the same roots are obtained")

Output -

R =

10.0000
-4.0000
2.0000

Hence the same roots are obtained

I hope my answer helps. Have a nice day