# 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).

edit retag close merge delete

Note that we write Sage rather than SAGE.

( 2016-11-02 16:56:35 +0200 )edit

Sort by ยป oldest newest most voted

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:

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

more

yes this is what I am looking for.. thank you..

( 2016-11-02 09:07:24 +0200 )edit

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():
....:
-36*I*sqrt(2) + 15
36*I*sqrt(2) + 15

more

Thank you for explaining this to me. It is so useful in my calculation.

( 2016-11-03 11:50:38 +0200 )edit

## Stats

Seen: 421 times

Last updated: Nov 03 '16