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Baldemy
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Why is the polyval command giving two different answers?

Asked by Baldemy
on 22 Sep 2014
Latest activity Commented on by Matt J
on 23 Sep 2014
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

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2 Answers

Answer by Alberto
on 22 Sep 2014
 Accepted Answer

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

  1 Comment

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

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Answer by Matt J
on 22 Sep 2014
Edited by Matt J
on 22 Sep 2014

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

  2 Comments

ok then this happens instead
>> 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
And what don't you like about it? The result is quite close to zero, as one would expect.

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