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).
yes this is what I am looking for.. thank you..
2 Answers
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:
x2−30x+2817=(x−(15−36√−2))(x−(15+36√−2))
Comments
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) + 15Comments
Thank you for explaining this to me. It is so useful in my calculation.
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Asked: 8 years ago
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Last updated: Nov 03 '16
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