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

Define the polynomial ring

$\Bbb Q[c][x]$ .Find the

$c$ values where

$x^2 + x + c + 1$ has a double root.

asked 5 years ago

Anonymous

updated 5 years ago

FrédéricC

5426 ●4 ●44 ●121

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

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 ( 5 years ago )

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answered 5 years ago

rburing

10964 ●4 ●80 ●219 https://www.rburing.nl/

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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Last updated: Jul 29 '19

Define the polynomial ring Q[c][x]\Bbb Q[c][x].Find the cc values where x2+x+c+1x^2 + x + c + 1 has a double root. savecancel

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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.