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What is the relationship between the degree of a polynomial and the number of roots it has?
In answering this question it is important that the roots are counted along with their multiplicity. Thus a double root is counted as two roots, and so on.
The degree of a polynomial is exactly the same as the number of roots that it has in the complex field.
If the polynomial has real coefficients, then a polynomial with an odd degree has
an odd number of roots up to the degree, while a polynomial of even degree has an even number of roots up to the degree. The difference between the degree and the number of roots is the number of complex roots which come as complex conjugate pairs.
What else can I help you with?
Is 13 a polynomial If it is find its degree and classify it by the number of its terms?
13 is not a polynomial.
What is the number which when substituted in a polynomial makes its value zero?
A root.
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - b is a factor?
a
What does Number Bonding mean?
A number bond is the relationship between a number and the parts that combine to make it.
What is the relationship between the rectangles for number and factors of the number?
One rectangle for each factor pair.
Is there a relationship between the degree of a polynomial and the number of times its graphed curve changes direction?
I think that there is not .
What is a zero degree polynomial called?
a polynomial of degree...............is called a cubic polynomial
Is the number of y-intercepts for a polynomial determined by the degree of the polynomial?
no...
Is 13 a polynomial If it is find its degree and classify it by the number of its terms?
13 is not a polynomial.
What is the leading coefficient in a polynomial?
It is the number (coefficient) that belongs to the variable of the highest degree in a polynomial.
What is the difference between Cardinality and Degree?
Degree the number of entity types that participate in a relationship.
What is the relationship between the degree and the number of roots counting multiplicities?
In the complex field, the two numbers are the same. If you restrict yourself to real solutions, the relationship is as follows: A polynomial of degree p has p-2k real solutions where k is an integer such that p-2k is non-negative. [There will be 2k pairs of complex conjugate roots.]
What is the classification of terms according to number and degree?
the degree of polynomial is determined by the highest exponent its variable has.
Classify the polynomial by its degree and by the number of terms.5m?
linear monomial
What is a single number that describes the degree of relationship between two variables?
Correlation
What is the minimum number of x-intercepts that a 7th degree polynomial might have?
1
Is it true that the degree of polynomial function determine the number of real roots?
Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)
