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How to find the roots of a polynomial when its coefficients are not integers?
Clash Royale CLAN TAG#URR8PPP
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How do you find the roots of a polynomial when the coefficients of a polynomial are not integers? I understand you cannot use the rational zero theorem here. So what other methods can be used here. Is there a series of methods, that all you to find the zeroes of any polynomial with decimals in them, no matter the situation? If so, what are the methods? If not, can you at least give me some methods?
By the way, can you please give your answer in simple enough form that it can be understand by a high school pre-calc student?
algebra-precalculus polynomials
edited Jul 17 at 13:26
steven gregory
16.5k22055
asked Jul 17 at 12:53
Ethan Chan
603322
 |Â
show 7 more comments
up vote
-1
down vote
favorite
How do you find the roots of a polynomial when the coefficients of a polynomial are not integers? I understand you cannot use the rational zero theorem here. So what other methods can be used here. Is there a series of methods, that all you to find the zeroes of any polynomial with decimals in them, no matter the situation? If so, what are the methods? If not, can you at least give me some methods?
By the way, can you please give your answer in simple enough form that it can be understand by a high school pre-calc student?
algebra-precalculus polynomials
edited Jul 17 at 13:26
steven gregory
16.5k22055
asked Jul 17 at 12:53
Ethan Chan
603322
There are methods of solving 2, 3, 4 degree equations. Usually polynomials of degree greater than $5$ are unsolvable by radicals. The other methods would be to just approximate a root. Note that methods of solving cubic and quartic equations can leave you with root of a complex number (even if the root is purely real).
– Rumpelstiltskin
Jul 17 at 12:56
I solve my degree 2 polynomials the exact same way no matter what the coefficients are: Integers, rational numbers, real numbers or complex. (Except in very simple integer cases.) $frac-bpmsqrtb^2-4ac2a$ works like a charm every time.
– Arthur
Jul 17 at 12:57
There is no general method for any degree $ge 5$ (and it does not mattter whether the coefficients are integer, rational, real or compex). There are numerical equation solvers (computer programs) however that can do most if not all of the heavy lifting in almost all cases.
– NickD
Jul 17 at 13:00
@NickD The result is that there is no general solution in radicals. This is different from "no general method".
– user574889
Jul 17 at 13:01
Yes, I misspoke.
– NickD
Jul 17 at 13:02
 |Â
show 7 more comments
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
How do you find the roots of a polynomial when the coefficients of a polynomial are not integers? I understand you cannot use the rational zero theorem here. So what other methods can be used here. Is there a series of methods, that all you to find the zeroes of any polynomial with decimals in them, no matter the situation? If so, what are the methods? If not, can you at least give me some methods?
By the way, can you please give your answer in simple enough form that it can be understand by a high school pre-calc student?
algebra-precalculus polynomials
edited Jul 17 at 13:26
steven gregory
16.5k22055
asked Jul 17 at 12:53
Ethan Chan
603322
How do you find the roots of a polynomial when the coefficients of a polynomial are not integers? I understand you cannot use the rational zero theorem here. So what other methods can be used here. Is there a series of methods, that all you to find the zeroes of any polynomial with decimals in them, no matter the situation? If so, what are the methods? If not, can you at least give me some methods?
By the way, can you please give your answer in simple enough form that it can be understand by a high school pre-calc student?
algebra-precalculus polynomials
edited Jul 17 at 13:26
steven gregory
16.5k22055
asked Jul 17 at 12:53
Ethan Chan
603322
edited Jul 17 at 13:26
steven gregory
16.5k22055
edited Jul 17 at 13:26
steven gregory
16.5k22055
edited Jul 17 at 13:26
steven gregory
16.5k22055
16.5k22055
asked Jul 17 at 12:53
Ethan Chan
603322
asked Jul 17 at 12:53
Ethan Chan
603322
asked Jul 17 at 12:53
Ethan Chan
603322
603322
There are methods of solving 2, 3, 4 degree equations. Usually polynomials of degree greater than $5$ are unsolvable by radicals. The other methods would be to just approximate a root. Note that methods of solving cubic and quartic equations can leave you with root of a complex number (even if the root is purely real).
– Rumpelstiltskin
Jul 17 at 12:56
I solve my degree 2 polynomials the exact same way no matter what the coefficients are: Integers, rational numbers, real numbers or complex. (Except in very simple integer cases.) $frac-bpmsqrtb^2-4ac2a$ works like a charm every time.
– Arthur
Jul 17 at 12:57
There is no general method for any degree $ge 5$ (and it does not mattter whether the coefficients are integer, rational, real or compex). There are numerical equation solvers (computer programs) however that can do most if not all of the heavy lifting in almost all cases.
– NickD
Jul 17 at 13:00
@NickD The result is that there is no general solution in radicals. This is different from "no general method".
– user574889
Jul 17 at 13:01
Yes, I misspoke.
– NickD
Jul 17 at 13:02
 |Â
show 7 more comments
There are methods of solving 2, 3, 4 degree equations. Usually polynomials of degree greater than $5$ are unsolvable by radicals. The other methods would be to just approximate a root. Note that methods of solving cubic and quartic equations can leave you with root of a complex number (even if the root is purely real).
– Rumpelstiltskin
Jul 17 at 12:56
I solve my degree 2 polynomials the exact same way no matter what the coefficients are: Integers, rational numbers, real numbers or complex. (Except in very simple integer cases.) $frac-bpmsqrtb^2-4ac2a$ works like a charm every time.
– Arthur
Jul 17 at 12:57
There is no general method for any degree $ge 5$ (and it does not mattter whether the coefficients are integer, rational, real or compex). There are numerical equation solvers (computer programs) however that can do most if not all of the heavy lifting in almost all cases.
– NickD
Jul 17 at 13:00
@NickD The result is that there is no general solution in radicals. This is different from "no general method".
– user574889
Jul 17 at 13:01
Yes, I misspoke.
– NickD
Jul 17 at 13:02
There are methods of solving 2, 3, 4 degree equations. Usually polynomials of degree greater than $5$ are unsolvable by radicals. The other methods would be to just approximate a root. Note that methods of solving cubic and quartic equations can leave you with root of a complex number (even if the root is purely real).
– Rumpelstiltskin
Jul 17 at 12:56
There are methods of solving 2, 3, 4 degree equations. Usually polynomials of degree greater than $5$ are unsolvable by radicals. The other methods would be to just approximate a root. Note that methods of solving cubic and quartic equations can leave you with root of a complex number (even if the root is purely real).
– Rumpelstiltskin
Jul 17 at 12:56
I solve my degree 2 polynomials the exact same way no matter what the coefficients are: Integers, rational numbers, real numbers or complex. (Except in very simple integer cases.) $frac-bpmsqrtb^2-4ac2a$ works like a charm every time.
– Arthur
Jul 17 at 12:57
I solve my degree 2 polynomials the exact same way no matter what the coefficients are: Integers, rational numbers, real numbers or complex. (Except in very simple integer cases.) $frac-bpmsqrtb^2-4ac2a$ works like a charm every time.
– Arthur
Jul 17 at 12:57
There is no general method for any degree $ge 5$ (and it does not mattter whether the coefficients are integer, rational, real or compex). There are numerical equation solvers (computer programs) however that can do most if not all of the heavy lifting in almost all cases.
– NickD
Jul 17 at 13:00
There is no general method for any degree $ge 5$ (and it does not mattter whether the coefficients are integer, rational, real or compex). There are numerical equation solvers (computer programs) however that can do most if not all of the heavy lifting in almost all cases.
– NickD
Jul 17 at 13:00
@NickD The result is that there is no general solution in radicals. This is different from "no general method".
– user574889
Jul 17 at 13:01
@NickD The result is that there is no general solution in radicals. This is different from "no general method".
– user574889
Jul 17 at 13:01
Yes, I misspoke.
– NickD
Jul 17 at 13:02
Yes, I misspoke.
– NickD
Jul 17 at 13:02
 |Â
show 7 more comments
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There are methods of solving 2, 3, 4 degree equations. Usually polynomials of degree greater than $5$ are unsolvable by radicals. The other methods would be to just approximate a root. Note that methods of solving cubic and quartic equations can leave you with root of a complex number (even if the root is purely real).
– Rumpelstiltskin
Jul 17 at 12:56
I solve my degree 2 polynomials the exact same way no matter what the coefficients are: Integers, rational numbers, real numbers or complex. (Except in very simple integer cases.) $frac-bpmsqrtb^2-4ac2a$ works like a charm every time.
– Arthur
Jul 17 at 12:57
There is no general method for any degree $ge 5$ (and it does not mattter whether the coefficients are integer, rational, real or compex). There are numerical equation solvers (computer programs) however that can do most if not all of the heavy lifting in almost all cases.
– NickD
Jul 17 at 13:00
@NickD The result is that there is no general solution in radicals. This is different from "no general method".
– user574889
Jul 17 at 13:01
Yes, I misspoke.
– NickD
Jul 17 at 13:02