# factor x^2 - 30*x + 2817 in sqrt(-2)

Is there a way I can use SAGE to factor my polynomial x^2 - 30*x + 2817 in sqrt(-2).

factor x^2 - 30*x + 2817 in sqrt(-2)

Is there a way I can use SAGE to factor my polynomial x^2 - 30*x + 2817 in sqrt(-2).

3

I think you are looking for the roots of the polynomial:

```
f = x^2 - 30*x + 2817
f.roots()
```

which gives:

```
[(-36*I*sqrt(2) + 15, 1), (36*I*sqrt(2) + 15, 1)]
```

This would mean that your original function is equal to:

$$ x^2-30x+2817 = \left(x-(15-36 \sqrt{-2})\right)\left(x-(15+36\sqrt{-2})\right)$$

1

Note that you can also work over the field QQbar of algebraic numbers.

Here is how you would factor your polynomial there and find its roots.

```
sage: P.<x> = QQbar[]
sage: p = x^2 - 30*x + 2817
sage: p.factor()
(x - 15.00000000000000? - 50.91168824543143?*I) * (x - 15.00000000000000? + 50.91168824543143?*I)
sage: p.roots()
[(15.00000000000000? - 50.91168824543143?*I, 1),
(15.00000000000000? + 50.91168824543143?*I, 1)]
```

If you want a radical expression for the roots:

```
sage: for r in p.roots():
....: print(r[0].radical_expression())
....:
-36*I*sqrt(2) + 15
36*I*sqrt(2) + 15
```

Please start posting anonymously - your entry will be published after you log in or create a new account.

Asked: ** 2016-11-02 06:47:32 +0200 **

Seen: **421 times**

Last updated: **Nov 03 '16**

Factoring bivariate polynomials w.r.t. a single variable

Factorization of non-commutative Laurent polynomials

out of core exact linear algebra

Polynomial: find the common factor

factor() issue with second degre polynomes

why don't sage return exact value in some functions

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.

Note that we write Sage rather than SAGE.