MATLAB: Is the polyval command giving two different answers

Question

Why does the polyval operator not work as expected. Is the ans variable not stored as a column vector? Why aren't the second, fifth, and sixth results equal?

>> roots([1,-8,17,2,-24])

ans =

    4.0000
    3.0000
    2.0000
   -1.0000

>> polyval([1.-8,17,2,-24],ans)

ans =

 -192.0000
  -54.0000
   -8.0000
   -2.0000

>> roots([1,-8,17,2,-24])

ans =

    4.0000
    3.0000
    2.0000
   -1.0000

>> x=ans

x =

    4.0000
    3.0000
    2.0000
   -1.0000

>> polyval([1,-8,17,2,-24],x)

ans =

   1.0e-13 *
    0.8882
    0.3197
    0.0355
    0.1421

>> polyval([1,-8,17,2,-24],[2.0000;3.0000;-1.0000;3])

ans =

     0
     0
     0
     0

Answer 1

Instruction roots uses an iterative numeric method to approximate the solution in float arithmetic. What you get is an excellent approximation.

If you need the exact solution you should try a symbolic method:

g = x^4-8*x^3 + 17*x^2 +2*x -24

g =

x^4 - 8*x^3 + 17*x^2 + 2*x - 24

>> sol=solve(g==0)

sol =

2
3
4
-1