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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.

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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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## Comments

Is it homework ?

( 2019-07-28 21:14:54 +0200 )edit

## 1 Answer

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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 15:00:01 +0200

Seen: 1,058 times

Last updated: Jul 29 '19