 
 
 
11.1.22  Exact roots of a polynomial
The roots command
finds roots of polynomials with their multiplicities.
- 
roots takes one mandatory and one optional argument:
- 
P, a symbolic polynomial expression.
- Optionally, x, the name of the variable (the default is
x).
 
- roots(P  ⟨,x⟩) returns a 2
column matrix: each row is the list consisting of a root of
P and its multiplicity.
Examples
Find the roots of P(x)=x5−2x4+x3.
|  | | |  | | ⎡ ⎢
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Find the roots of
x10−15x8+90x6−270x4+405x2−243=(x2−3)5.
| roots(x^10-15*x^8+90*x^6-270*x^4+405*x^2-243) | 
|  | | |  | | ⎡ ⎢
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Find the roots of t3−1.
|  | | |  | | ⎡ ⎢
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