Finding sum of some fractional powers(1/5) of root of polynomial
up vote
1
down vote
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Do we have some proper method to find sum of roots of the root of P(x)?
Like say
we have P(x) =$ x^3 -16x^2 + 57x+1$
say its root are a,b, c
for finding $ a^{1/5} + b^ {1/5} +c^{1/5} $
do we have some method or i need to take power 5 and
solve manipulating the terms ?
algebra-precalculus
asked Nov 17 at 20:36
maveric
61611
|
show 1 more comment
up vote
1
down vote
favorite
Do we have some proper method to find sum of roots of the root of P(x)?
Like say
we have P(x) =$ x^3 -16x^2 + 57x+1$
say its root are a,b, c
for finding $ a^{1/5} + b^ {1/5} +c^{1/5} $
do we have some method or i need to take power 5 and
solve manipulating the terms ?
algebra-precalculus
asked Nov 17 at 20:36
maveric
61611
Interesting. I would think there might be some results as an application of vieta's formula's
– Mason
Nov 17 at 20:58
desmos.com/calculator/x29fcpfahk
– Mason
Nov 17 at 21:09
No. I would think that there is not a general method of doing this: You will have to compute the roots and then compute the powers. For a polynomials with degree less than $4$ there is a formula for finding the roots: and thereby there is a formula for the sum of the roots raised to some power. For higher degree polynomials there is not a formula for this.
– Mason
Nov 17 at 21:33
so here can we find the value?
– maveric
Nov 18 at 5:26
Very similar to Sum of fifth roots of roots of cubic.
– mathlove
Nov 18 at 6:08
|
show 1 more comment
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Do we have some proper method to find sum of roots of the root of P(x)?
Like say
we have P(x) =$ x^3 -16x^2 + 57x+1$
say its root are a,b, c
for finding $ a^{1/5} + b^ {1/5} +c^{1/5} $
do we have some method or i need to take power 5 and
solve manipulating the terms ?
algebra-precalculus
asked Nov 17 at 20:36
maveric
61611
Do we have some proper method to find sum of roots of the root of P(x)?
Like say
we have P(x) =$ x^3 -16x^2 + 57x+1$
say its root are a,b, c
for finding $ a^{1/5} + b^ {1/5} +c^{1/5} $
do we have some method or i need to take power 5 and
solve manipulating the terms ?
algebra-precalculus
algebra-precalculus
asked Nov 17 at 20:36
maveric
61611
asked Nov 17 at 20:36
maveric
61611
edited Nov 17 at 20:42
asked Nov 17 at 20:36
maveric
61611
asked Nov 17 at 20:36
maveric
61611
asked Nov 17 at 20:36
maveric
61611
61611
Interesting. I would think there might be some results as an application of vieta's formula's
– Mason
Nov 17 at 20:58
desmos.com/calculator/x29fcpfahk
– Mason
Nov 17 at 21:09
No. I would think that there is not a general method of doing this: You will have to compute the roots and then compute the powers. For a polynomials with degree less than $4$ there is a formula for finding the roots: and thereby there is a formula for the sum of the roots raised to some power. For higher degree polynomials there is not a formula for this.
– Mason
Nov 17 at 21:33
so here can we find the value?
– maveric
Nov 18 at 5:26
Very similar to Sum of fifth roots of roots of cubic.
– mathlove
Nov 18 at 6:08
|
show 1 more comment
Interesting. I would think there might be some results as an application of vieta's formula's
– Mason
Nov 17 at 20:58
desmos.com/calculator/x29fcpfahk
– Mason
Nov 17 at 21:09
No. I would think that there is not a general method of doing this: You will have to compute the roots and then compute the powers. For a polynomials with degree less than $4$ there is a formula for finding the roots: and thereby there is a formula for the sum of the roots raised to some power. For higher degree polynomials there is not a formula for this.
– Mason
Nov 17 at 21:33
so here can we find the value?
– maveric
Nov 18 at 5:26
Very similar to Sum of fifth roots of roots of cubic.
– mathlove
Nov 18 at 6:08
Interesting. I would think there might be some results as an application of vieta's formula's
– Mason
Nov 17 at 20:58
Interesting. I would think there might be some results as an application of vieta's formula's
– Mason
Nov 17 at 20:58
desmos.com/calculator/x29fcpfahk
– Mason
Nov 17 at 21:09
desmos.com/calculator/x29fcpfahk
– Mason
Nov 17 at 21:09
No. I would think that there is not a general method of doing this: You will have to compute the roots and then compute the powers. For a polynomials with degree less than $4$ there is a formula for finding the roots: and thereby there is a formula for the sum of the roots raised to some power. For higher degree polynomials there is not a formula for this.
– Mason
Nov 17 at 21:33
No. I would think that there is not a general method of doing this: You will have to compute the roots and then compute the powers. For a polynomials with degree less than $4$ there is a formula for finding the roots: and thereby there is a formula for the sum of the roots raised to some power. For higher degree polynomials there is not a formula for this.
– Mason
Nov 17 at 21:33
so here can we find the value?
– maveric
Nov 18 at 5:26
so here can we find the value?
– maveric
Nov 18 at 5:26
Very similar to Sum of fifth roots of roots of cubic.
– mathlove
Nov 18 at 6:08
Very similar to Sum of fifth roots of roots of cubic.
– mathlove
Nov 18 at 6:08
|
show 1 more comment
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Interesting. I would think there might be some results as an application of vieta's formula's
– Mason
Nov 17 at 20:58
desmos.com/calculator/x29fcpfahk
– Mason
Nov 17 at 21:09
No. I would think that there is not a general method of doing this: You will have to compute the roots and then compute the powers. For a polynomials with degree less than $4$ there is a formula for finding the roots: and thereby there is a formula for the sum of the roots raised to some power. For higher degree polynomials there is not a formula for this.
– Mason
Nov 17 at 21:33
so here can we find the value?
– maveric
Nov 18 at 5:26
Very similar to Sum of fifth roots of roots of cubic.
– mathlove
Nov 18 at 6:08