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Order of polynomial, unique number of equations needed
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I am doing Linear Algebra and am working on a homework assignment and am quite confused.
The question is:
Recall that R(x) is a rational function <-> R(x) = P(x)/Q(x) such that
P(x) & Q(x) are each polynomials. If the order of P(x) = O[P(x)] = p
and O[Q(x)] = q, then, using p and q in your answer, what is the
minimum number of unique equations required to solve for R(x)?
I asked the teacher for clarification as I am quite confused and he replied:
What does order refer to? What does it mean? I need to consider that
with regards to polynomials and how many unique equations you need to
solve for those polynomials… This is related to their order.
I understand that order is the highest power that a polynomial is raised to.
However I am completely lost with regards to the number of unique equations needed. Can anyone give me a push in the right direction?
EDIT: I understand that a polynomial of order 2 can be rewritten as the factor of its zeroes with 2 factors, order 3 can be rewritten as the factor of its zeroes with 3 factors, and so on.
However I am still a bit confused.
Would the expression in terms of p and q defined above be (np)/(mq) where n is the order of the equation in the numerator and m is order of the equation in the denominator?
linear-algebra
asked Jul 26 at 18:42
Ross Satchell
41
 |Â
show 4 more comments
up vote
0
down vote
favorite
I am doing Linear Algebra and am working on a homework assignment and am quite confused.
The question is:
Recall that R(x) is a rational function <-> R(x) = P(x)/Q(x) such that
P(x) & Q(x) are each polynomials. If the order of P(x) = O[P(x)] = p
and O[Q(x)] = q, then, using p and q in your answer, what is the
minimum number of unique equations required to solve for R(x)?
I asked the teacher for clarification as I am quite confused and he replied:
What does order refer to? What does it mean? I need to consider that
with regards to polynomials and how many unique equations you need to
solve for those polynomials… This is related to their order.
I understand that order is the highest power that a polynomial is raised to.
However I am completely lost with regards to the number of unique equations needed. Can anyone give me a push in the right direction?
EDIT: I understand that a polynomial of order 2 can be rewritten as the factor of its zeroes with 2 factors, order 3 can be rewritten as the factor of its zeroes with 3 factors, and so on.
However I am still a bit confused.
Would the expression in terms of p and q defined above be (np)/(mq) where n is the order of the equation in the numerator and m is order of the equation in the denominator?
linear-algebra
asked Jul 26 at 18:42
Ross Satchell
41
How many roots or zeroes does a polynomial of order p have? Then how can you rewrite the polynomial as factor of its zeroes?...hope this helps...
– Pi_die_die
Jul 26 at 18:46
I have to admit that I don’t even understand the question... what means * ...equations to solve for $R(x)$*?
– mathcounterexamples.net
Jul 26 at 19:20
Forget about rationals functions for the moment and try to solve the same question for polynomials (or rational functions with constant denominator.) How many equations do you need to determine a line? a parabola? a polynomial of degree $n$? How does your answer change if you have a rational function?
– saulspatz
Jul 26 at 19:34
@mathcounterexamples.net Equations like $R(x_1)=y_1, R(x_2)=y_2,$ etc.
– saulspatz
Jul 26 at 19:39
@Pi_die_die I have edited the question to update my understanding.
– Ross Satchell
Jul 26 at 20:07
 |Â
show 4 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am doing Linear Algebra and am working on a homework assignment and am quite confused.
The question is:
Recall that R(x) is a rational function <-> R(x) = P(x)/Q(x) such that
P(x) & Q(x) are each polynomials. If the order of P(x) = O[P(x)] = p
and O[Q(x)] = q, then, using p and q in your answer, what is the
minimum number of unique equations required to solve for R(x)?
I asked the teacher for clarification as I am quite confused and he replied:
What does order refer to? What does it mean? I need to consider that
with regards to polynomials and how many unique equations you need to
solve for those polynomials… This is related to their order.
I understand that order is the highest power that a polynomial is raised to.
However I am completely lost with regards to the number of unique equations needed. Can anyone give me a push in the right direction?
EDIT: I understand that a polynomial of order 2 can be rewritten as the factor of its zeroes with 2 factors, order 3 can be rewritten as the factor of its zeroes with 3 factors, and so on.
However I am still a bit confused.
Would the expression in terms of p and q defined above be (np)/(mq) where n is the order of the equation in the numerator and m is order of the equation in the denominator?
linear-algebra
asked Jul 26 at 18:42
Ross Satchell
41
I am doing Linear Algebra and am working on a homework assignment and am quite confused.
The question is:
Recall that R(x) is a rational function <-> R(x) = P(x)/Q(x) such that
P(x) & Q(x) are each polynomials. If the order of P(x) = O[P(x)] = p
and O[Q(x)] = q, then, using p and q in your answer, what is the
minimum number of unique equations required to solve for R(x)?
I asked the teacher for clarification as I am quite confused and he replied:
What does order refer to? What does it mean? I need to consider that
with regards to polynomials and how many unique equations you need to
solve for those polynomials… This is related to their order.
I understand that order is the highest power that a polynomial is raised to.
However I am completely lost with regards to the number of unique equations needed. Can anyone give me a push in the right direction?
EDIT: I understand that a polynomial of order 2 can be rewritten as the factor of its zeroes with 2 factors, order 3 can be rewritten as the factor of its zeroes with 3 factors, and so on.
However I am still a bit confused.
Would the expression in terms of p and q defined above be (np)/(mq) where n is the order of the equation in the numerator and m is order of the equation in the denominator?
linear-algebra
asked Jul 26 at 18:42
Ross Satchell
41
edited Jul 26 at 20:06
asked Jul 26 at 18:42
Ross Satchell
41
asked Jul 26 at 18:42
Ross Satchell
41
asked Jul 26 at 18:42
Ross Satchell
41
41
How many roots or zeroes does a polynomial of order p have? Then how can you rewrite the polynomial as factor of its zeroes?...hope this helps...
– Pi_die_die
Jul 26 at 18:46
I have to admit that I don’t even understand the question... what means * ...equations to solve for $R(x)$*?
– mathcounterexamples.net
Jul 26 at 19:20
Forget about rationals functions for the moment and try to solve the same question for polynomials (or rational functions with constant denominator.) How many equations do you need to determine a line? a parabola? a polynomial of degree $n$? How does your answer change if you have a rational function?
– saulspatz
Jul 26 at 19:34
@mathcounterexamples.net Equations like $R(x_1)=y_1, R(x_2)=y_2,$ etc.
– saulspatz
Jul 26 at 19:39
@Pi_die_die I have edited the question to update my understanding.
– Ross Satchell
Jul 26 at 20:07
 |Â
show 4 more comments
How many roots or zeroes does a polynomial of order p have? Then how can you rewrite the polynomial as factor of its zeroes?...hope this helps...
– Pi_die_die
Jul 26 at 18:46
I have to admit that I don’t even understand the question... what means * ...equations to solve for $R(x)$*?
– mathcounterexamples.net
Jul 26 at 19:20
Forget about rationals functions for the moment and try to solve the same question for polynomials (or rational functions with constant denominator.) How many equations do you need to determine a line? a parabola? a polynomial of degree $n$? How does your answer change if you have a rational function?
– saulspatz
Jul 26 at 19:34
@mathcounterexamples.net Equations like $R(x_1)=y_1, R(x_2)=y_2,$ etc.
– saulspatz
Jul 26 at 19:39
@Pi_die_die I have edited the question to update my understanding.
– Ross Satchell
Jul 26 at 20:07
How many roots or zeroes does a polynomial of order p have? Then how can you rewrite the polynomial as factor of its zeroes?...hope this helps...
– Pi_die_die
Jul 26 at 18:46
How many roots or zeroes does a polynomial of order p have? Then how can you rewrite the polynomial as factor of its zeroes?...hope this helps...
– Pi_die_die
Jul 26 at 18:46
I have to admit that I don’t even understand the question... what means * ...equations to solve for $R(x)$*?
– mathcounterexamples.net
Jul 26 at 19:20
I have to admit that I don’t even understand the question... what means * ...equations to solve for $R(x)$*?
– mathcounterexamples.net
Jul 26 at 19:20
Forget about rationals functions for the moment and try to solve the same question for polynomials (or rational functions with constant denominator.) How many equations do you need to determine a line? a parabola? a polynomial of degree $n$? How does your answer change if you have a rational function?
– saulspatz
Jul 26 at 19:34
Forget about rationals functions for the moment and try to solve the same question for polynomials (or rational functions with constant denominator.) How many equations do you need to determine a line? a parabola? a polynomial of degree $n$? How does your answer change if you have a rational function?
– saulspatz
Jul 26 at 19:34
@mathcounterexamples.net Equations like $R(x_1)=y_1, R(x_2)=y_2,$ etc.
– saulspatz
Jul 26 at 19:39
@mathcounterexamples.net Equations like $R(x_1)=y_1, R(x_2)=y_2,$ etc.
– saulspatz
Jul 26 at 19:39
@Pi_die_die I have edited the question to update my understanding.
– Ross Satchell
Jul 26 at 20:07
@Pi_die_die I have edited the question to update my understanding.
– Ross Satchell
Jul 26 at 20:07
 |Â
show 4 more comments
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How many roots or zeroes does a polynomial of order p have? Then how can you rewrite the polynomial as factor of its zeroes?...hope this helps...
– Pi_die_die
Jul 26 at 18:46
I have to admit that I don’t even understand the question... what means * ...equations to solve for $R(x)$*?
– mathcounterexamples.net
Jul 26 at 19:20
Forget about rationals functions for the moment and try to solve the same question for polynomials (or rational functions with constant denominator.) How many equations do you need to determine a line? a parabola? a polynomial of degree $n$? How does your answer change if you have a rational function?
– saulspatz
Jul 26 at 19:34
@mathcounterexamples.net Equations like $R(x_1)=y_1, R(x_2)=y_2,$ etc.
– saulspatz
Jul 26 at 19:39
@Pi_die_die I have edited the question to update my understanding.
– Ross Satchell
Jul 26 at 20:07