###### Asked in Algebra

Algebra

# What is the minimum number of x-intercepts that a 7th degree polynomial might have?

## Answer

###### Wiki User

###### May 08, 2012 1:21PM

1

## Related Questions

###### Asked in Math and Arithmetic, Algebra, Factoring and Multiples

### 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.

###### Asked in Math and Arithmetic, Algebra

### What is the missing number 7 16 8 27 9?

The answer depends on where, in the sequence, the missing number
is meant to go.
Furthermore, whatever number you choose and wherever in the
sequence it is meant to be, it is always possible to find a
polynomial of degree 5 that will go through all five points given
in the question and your chosen one.
Using a polynomial of degree 4, the next number is -218.
The answer depends on where, in the sequence, the missing number is
meant to go.
Furthermore, whatever number you choose and wherever in the
sequence it is meant to be, it is always possible to find a
polynomial of degree 5 that will go through all five points given
in the question and your chosen one.
Using a polynomial of degree 4, the next number is -218.
The answer depends on where, in the sequence, the missing number is
meant to go.
Furthermore, whatever number you choose and wherever in the
sequence it is meant to be, it is always possible to find a
polynomial of degree 5 that will go through all five points given
in the question and your chosen one.
Using a polynomial of degree 4, the next number is -218.
The answer depends on where, in the sequence, the missing number is
meant to go.
Furthermore, whatever number you choose and wherever in the
sequence it is meant to be, it is always possible to find a
polynomial of degree 5 that will go through all five points given
in the question and your chosen one.
Using a polynomial of degree 4, the next number is -218.

###### Asked in Math and Arithmetic, Algebra

### 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.)

###### Asked in Math and Arithmetic, Algebra, Geometry

### What are quadratic polynomial quartic polynomial constant polynomial and quintic polynomial?

Those words refer to the degree, or highest exponent that
modifies a variable, or the polynomial.
Constant=No variables in the polynomial
Linear=Variable raised to the first power
Quadratic=Variable raised to the second power (or "squared")
Cubic=Variable raised to the third power (or "cubed")
Quartic=Variable raised to the fourth power
Quintic=Variable raised to the fifth power
Anything higher than that is known as a "6th-degree" polynomial,
or "21st-degree" polynomial. It all depends on the highest exponent
in the polynomial. Remember, exponents modifying a constant (normal
number) do not count.

###### Asked in Math and Arithmetic

### What is the next number in this series 3 -6 12 4 20?

It is possible to select any real number and then find a
polynomial of degree 5 which will have that number as the next
number in the sequence. And there are other functional forms as
well.
Using the polynomial
Un = (103n4 - 1242n3 + 5201x2 - 8670x + 4680)/24 where n = 1, 2,
3, ...
the next number would be 213
It is possible to select any real number and then find a
polynomial of degree 5 which will have that number as the next
number in the sequence. And there are other functional forms as
well.
Using the polynomial
Un = (103n4 - 1242n3 + 5201x2 - 8670x + 4680)/24 where n = 1, 2,
3, ...
the next number would be 213
It is possible to select any real number and then find a
polynomial of degree 5 which will have that number as the next
number in the sequence. And there are other functional forms as
well.
Using the polynomial
Un = (103n4 - 1242n3 + 5201x2 - 8670x + 4680)/24 where n = 1, 2,
3, ...
the next number would be 213
It is possible to select any real number and then find a
polynomial of degree 5 which will have that number as the next
number in the sequence. And there are other functional forms as
well.
Using the polynomial
Un = (103n4 - 1242n3 + 5201x2 - 8670x + 4680)/24 where n = 1, 2,
3, ...
the next number would be 213

###### Asked in Algebra

### A fourth degree polynomial that has five terms could have five linear factors.?

No, if it is of degree 4, it can have 4 linear factors,
regardless of the number of terms.For example, x squared + 5x + 6 =
(x+3)(x+2). The unfactored polynomial has three terms, and is of
degree 2. Similarly, you can multiply four linear terms together;
and you will get a polynomial of degree 4, which has up to 5
terms.

###### Asked in Math and Arithmetic

### What comes next in series 2 2 4 12 16 80?

It depends on which number you would like to be the next in the
sequence. Choose any real number and it is possible to find a
polynomial of degree 6 that will generate the above six numbers and
the selected seventh.
Using a polynomial of degree 5:
Un = (44n5 - 695n4 + 4130n3 - 11305n2 + 14066n - 6120)/60 for n
= 1, 2, 3, ...
forces the next number to be 430.
It depends on which number you would like to be the next in the
sequence. Choose any real number and it is possible to find a
polynomial of degree 6 that will generate the above six numbers and
the selected seventh.
Using a polynomial of degree 5:
Un = (44n5 - 695n4 + 4130n3 - 11305n2 + 14066n - 6120)/60 for n
= 1, 2, 3, ...
forces the next number to be 430.
It depends on which number you would like to be the next in the
sequence. Choose any real number and it is possible to find a
polynomial of degree 6 that will generate the above six numbers and
the selected seventh.
Using a polynomial of degree 5:
Un = (44n5 - 695n4 + 4130n3 - 11305n2 + 14066n - 6120)/60 for n
= 1, 2, 3, ...
forces the next number to be 430.
It depends on which number you would like to be the next in the
sequence. Choose any real number and it is possible to find a
polynomial of degree 6 that will generate the above six numbers and
the selected seventh.
Using a polynomial of degree 5:
Un = (44n5 - 695n4 + 4130n3 - 11305n2 + 14066n - 6120)/60 for n
= 1, 2, 3, ...
forces the next number to be 430.

###### Asked in Math and Arithmetic

### Can there be two patterns in a sequence?

Yes, there can be infinitely many. Given a sequence of n numbers,
it is always possible to fit a polynomial of degree (n-1) to it.
That polynomial is one posible pattern.
Then suppose the sequence is extended by adding an (n+1)thnumber
= k. You now have a sequence of n+1 numbers and there is a
polynomial of degree n that will fit it. For each of an infinite
number of values of k, there will be a different polynomial of
degree n. Next add another number, l. There will now be an infinite
number of polynomials of degree n+1. And this process can continue
without end.
And these are only polynomial functions. You can have other
rules - for example, sums of sines and cosines (see Fourier
transformations if you are really keen and able).

###### Asked in Math and Arithmetic

### What number comes after 3 -6 12 4 20?

Given any number, it is possible to find a polynomial of degree
5 that will generate the above sequence of numbers and the
additional sixth. There are also non-polynomial rules possible.
The polynomial of degree 4 that will generate this sequence
is
Un = (103n4 - 1242n3 + 5201n2 - 8670n + 4680)/24 for n = 1, 2,
3, ... and, according to this rule, the next number is 213.

###### Asked in Math and Arithmetic, Algebra

### What is next number is series 298 209 129 58 - 4?

The answer can be any number that you like: it is always
possible to find a polynomial of order 5 to fit the given numbers
and any other number.
The lowest degree polynomial that will fit the given numbers is
the quadratic
Un = (9n2 - 205n + 792)/2 for n = 1, 2, 3, .. . and that gives
the next number as -57.
The answer can be any number that you like: it is always possible
to find a polynomial of order 5 to fit the given numbers and
any other number.
The lowest degree polynomial that will fit the given numbers is
the quadratic
Un = (9n2 - 205n + 792)/2 for n = 1, 2, 3, .. . and that gives
the next number as -57.
The answer can be any number that you like: it is always possible
to find a polynomial of order 5 to fit the given numbers and
any other number.
The lowest degree polynomial that will fit the given numbers is
the quadratic
Un = (9n2 - 205n + 792)/2 for n = 1, 2, 3, .. . and that gives
the next number as -57.
The answer can be any number that you like: it is always possible
to find a polynomial of order 5 to fit the given numbers and
any other number.
The lowest degree polynomial that will fit the given numbers is
the quadratic
Un = (9n2 - 205n + 792)/2 for n = 1, 2, 3, .. . and that gives
the next number as -57.

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