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.

Find the roots of P(x)=x⁵−2x⁴+x³.

roots(x^5-16*x^4+x^3)

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎣

√

−3

√

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦

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.

roots(t^3-1,t)

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

√

−1

−i

√

−1

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦