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.
|
| |
| ⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎣ | | ⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦ |
|
| | | | | | | | | | |
|
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) |
|
| |
| ⎡
⎢
⎢
⎢
⎢
⎢
⎣ | | ⎤
⎥
⎥
⎥
⎥
⎥
⎦ |
|
| | | | | | | | | | |
|
Find the roots of t3−1.
|
| |
| ⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣ | | ⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦ |
|
| | | | | | | | | | |
|