MATLAB Function Reference |

**Syntax**

**Description**

returns a column vector whose elements are the roots of the polynomial ```
r = roots(c)
```

`c`

.

Row vector `c`

contains the coefficients of a polynomial, ordered in descending powers. If `c`

has `n+1`

components, the polynomial it represents is .

**Remarks**

Note the relationship of this function to `p = poly(r)`

, which returns a row vector whose elements are the coefficients of the polynomial. For vectors, `roots`

and `poly`

are inverse functions of each other, up to ordering, scaling, and roundoff error.

**Examples**

The polynomial is represented in MATLAB as

The roots of this polynomial are returned in a column vector by

**Algorithm**

The algorithm simply involves computing the eigenvalues of the companion matrix:

It is possible to prove that the results produced are the exact eigenvalues of a matrix within roundoff error of the companion matrix `A`

, but this does not mean that they are the exact roots of a polynomial with coefficients within roundoff error of those in `c`

.

**See Also**

Root Properties | rose |