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How to split the polynomial .
How to find all elements of a factor group?Split groups and quasi-split groups.Definition of split of exact sequenceIrreducibility of a cubic polynomialDetermine the irreducibility of polynomial.How to find the minimal polynomial.polynomial with a root but no linear factorReducing polynomial modulo $n$Finding minimal polynomial when the straight equation must be reduced.Splitting field of polynomial is F8
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$begingroup$
How do I split $x^2-5 $ in $mathbbZ/5mathbbZ$ ? Since $0$ is a root I have $x $ as linear factor . How can I find the other linear factor ?
abstract-algebra number-theory
asked 9 hours ago
AnabolicHorseAnabolicHorse
1708 bronze badges
$endgroup$
add a comment |
$begingroup$
How do I split $x^2-5 $ in $mathbbZ/5mathbbZ$ ? Since $0$ is a root I have $x $ as linear factor . How can I find the other linear factor ?
abstract-algebra number-theory
asked 9 hours ago
AnabolicHorseAnabolicHorse
1708 bronze badges
$endgroup$
1
$begingroup$
$x^2=xtimes x$
$endgroup$
– J. W. Tanner
9 hours ago
add a comment |
$begingroup$
How do I split $x^2-5 $ in $mathbbZ/5mathbbZ$ ? Since $0$ is a root I have $x $ as linear factor . How can I find the other linear factor ?
abstract-algebra number-theory
asked 9 hours ago
AnabolicHorseAnabolicHorse
1708 bronze badges
$endgroup$
How do I split $x^2-5 $ in $mathbbZ/5mathbbZ$ ? Since $0$ is a root I have $x $ as linear factor . How can I find the other linear factor ?
abstract-algebra number-theory
abstract-algebra number-theory
asked 9 hours ago
AnabolicHorseAnabolicHorse
1708 bronze badges
asked 9 hours ago
AnabolicHorseAnabolicHorse
1708 bronze badges
asked 9 hours ago
AnabolicHorseAnabolicHorse
1708 bronze badges
asked 9 hours ago
AnabolicHorseAnabolicHorse
1708 bronze badges
asked 9 hours ago
AnabolicHorseAnabolicHorse
1708 bronze badges
1708 bronze badges
1
$begingroup$
$x^2=xtimes x$
$endgroup$
– J. W. Tanner
9 hours ago
add a comment |
1
$begingroup$
$x^2=xtimes x$
$endgroup$
– J. W. Tanner
9 hours ago
1
1
$begingroup$
$x^2=xtimes x$
$endgroup$
– J. W. Tanner
9 hours ago
$begingroup$
$x^2=xtimes x$
$endgroup$
– J. W. Tanner
9 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Note that $x^2-5 = x^2$, which is already factorised.
answered 9 hours ago
Patrick StevensPatrick Stevens
29.4k5 gold badges29 silver badges75 bronze badges
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add a comment |
$begingroup$
Hint: Vieta's formulas still work. The sum of the two roots equals the (negative of the) coefficient of the first degree term.
answered 9 hours ago
ArthurArthur
132k9 gold badges127 silver badges219 bronze badges
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2 Answers
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2 Answers
2
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$begingroup$
Note that $x^2-5 = x^2$, which is already factorised.
answered 9 hours ago
Patrick StevensPatrick Stevens
29.4k5 gold badges29 silver badges75 bronze badges
$endgroup$
add a comment |
$begingroup$
Note that $x^2-5 = x^2$, which is already factorised.
answered 9 hours ago
Patrick StevensPatrick Stevens
29.4k5 gold badges29 silver badges75 bronze badges
$endgroup$
add a comment |
$begingroup$
Note that $x^2-5 = x^2$, which is already factorised.
answered 9 hours ago
Patrick StevensPatrick Stevens
29.4k5 gold badges29 silver badges75 bronze badges
$endgroup$
Note that $x^2-5 = x^2$, which is already factorised.
answered 9 hours ago
Patrick StevensPatrick Stevens
29.4k5 gold badges29 silver badges75 bronze badges
answered 9 hours ago
Patrick StevensPatrick Stevens
29.4k5 gold badges29 silver badges75 bronze badges
answered 9 hours ago
Patrick StevensPatrick Stevens
29.4k5 gold badges29 silver badges75 bronze badges
answered 9 hours ago
Patrick StevensPatrick Stevens
29.4k5 gold badges29 silver badges75 bronze badges
29.4k5 gold badges29 silver badges75 bronze badges
add a comment |
add a comment |
$begingroup$
Hint: Vieta's formulas still work. The sum of the two roots equals the (negative of the) coefficient of the first degree term.
answered 9 hours ago
ArthurArthur
132k9 gold badges127 silver badges219 bronze badges
$endgroup$
add a comment |
$begingroup$
Hint: Vieta's formulas still work. The sum of the two roots equals the (negative of the) coefficient of the first degree term.
answered 9 hours ago
ArthurArthur
132k9 gold badges127 silver badges219 bronze badges
$endgroup$
add a comment |
$begingroup$
Hint: Vieta's formulas still work. The sum of the two roots equals the (negative of the) coefficient of the first degree term.
answered 9 hours ago
ArthurArthur
132k9 gold badges127 silver badges219 bronze badges
$endgroup$
Hint: Vieta's formulas still work. The sum of the two roots equals the (negative of the) coefficient of the first degree term.
answered 9 hours ago
ArthurArthur
132k9 gold badges127 silver badges219 bronze badges
answered 9 hours ago
ArthurArthur
132k9 gold badges127 silver badges219 bronze badges
answered 9 hours ago
ArthurArthur
132k9 gold badges127 silver badges219 bronze badges
answered 9 hours ago
ArthurArthur
132k9 gold badges127 silver badges219 bronze badges
132k9 gold badges127 silver badges219 bronze badges
add a comment |
add a comment |
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1
$begingroup$
$x^2=xtimes x$
$endgroup$
– J. W. Tanner
9 hours ago