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Define the polynomial ring $\Bbb Q[c][x]$.Find the $c$ values where $x^2 + x + c + 1$ has a double root.

asked 2019-07-25 08:00:01 -0500

anonymous user

Anonymous

updated 2019-07-29 08:04:22 -0500

FrédéricC gravatar image

Sage question: Define the polynomial ring $\Bbb Q[c][x]$.Find the $c$ values where $x^2 + x + c + 1$ has a double root. Sage code I have found.

K.<c>=QQ['c']

R.<x>=K[]

f=x^2+x+c+1

f

How do I find the code for the $c$ values where $x^2 + x + c + 1$ has a double root. Also, can you give some examples so that I can construct some programming code in sage?

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Is it homework ?

tmonteil gravatar imagetmonteil ( 2019-07-28 14:14:54 -0500 )edit

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answered 2019-07-29 07:58:39 -0500

rburing gravatar image

A polynomial has a double root iff its discriminant is zero, so:

sage: f.discriminant()
-4*c - 3
sage: f.discriminant().roots(multiplicities=False)
[-3/4]
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Asked: 2019-07-25 08:00:01 -0500

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Last updated: Jul 29 '19