## Why is the polyval command giving two different answers?

### Baldemy (view profile)

on 22 Sep 2014
Latest activity Commented on by Matt J

on 23 Sep 2014

### Alberto (view profile)

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

### Alberto (view profile)

on 22 Sep 2014

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

Matt J

### Matt J (view profile)

on 23 Sep 2014
You also may need a symbolic version of polyval, even when you have the exact roots:
>> polyval([1,-8,17,2,-24]/3,[4 3 2 -1])
ans =
1.0e-14 *
0.8882 0.1776 0.1776 0.1776

on 22 Sep 2014
Edited by Matt J

### Matt J (view profile)

on 22 Sep 2014

Because you have a typo in your call to polyval: a period appears where a comma should be.

Baldemy

### Baldemy (view profile)

on 22 Sep 2014
>> roots([1,-8,17,2,-24])
ans =
4.000000000000009
2.999999999999992
2.000000000000001
-1.000000000000000
>> polyval([1,-8,17,2,-24],ans)
ans =
1.0e-13 *
0.888178419700125
0.319744231092045
0.035527136788005
0.142108547152020
Matt J

### Matt J (view profile)

on 22 Sep 2014
And what don't you like about it? The result is quite close to zero, as one would expect.