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Is it possible to find a polynomial of degree 3 that has -2 as its only real zero?
Wiki User
∙ 12y ago
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Kayleigh Padberg
Wiki User
∙ 12y agoA root of a polynomial can be found when the same polynomial is set equal to zero and factorised.
If x = -2 is a root then (x - (-2)) = (x + 2) is a factor.
So for a polynomial of degree three where x = -2 is the only root (repeated root)
then the polynomial is, (x + 2)3 = 0 which expands to, x3 + 6x2 + 12x + 8 = 0.
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What is the polynomial degree of 4ab5 2ab-3a4b3?
To find the polynomial degree you have only to add the exponents of all of the different components of the polynomial. In your case, you would add 1 and 5 from 4ab5 to get 6, 1 and 1 from 2ab to get 2, and 4 and 3 from 3a4b3 to get 7. Since the degree of the third component is the highest, that is you're answer.
Is it possible to find the discriminant of a binomial?
A polynomial discriminant is defined in terms of the difference in the roots of the polynomial equation. Since a binomial has only one root, there is nothing to take its difference from and so in such a situation, the discriminant is a meaningless concept.
What are the steps to solve these problems Find the degree of each polynomial 5a-2b2 plus 1 and 24xy-xy3 plus x2?
The degree of a polynomial function is the highest power any single term is raised to. For example, (5a - 2b^2) is a second degree function because the "b^2" is raised to the second power and the "a" is only raised to the (implied) first power. For (24xy-xy^3 + x^2) it is a third degree polynomial because the highest power is the cube of -xy.
Is it possible for a polynomial function of degree 3 to have no real zeros?
Yes - but only if the domain is restricted. Normally the domain is the whole of the real numbers and over that domain it must have at least one real zero.
Is -4 a polynomial?
is -4 a polynomial? This depends on what you accept as a definition A polynomial is often defined as a set of things in order obeying certain rules. ( these things and rules can be very complicated) A polynomial EQUATION is an equation between two polynomials When using only real numbers and "regular" math rules -4 is a polymomial of degree 0 x = -4 is a polynomial equation is a polynomial of degree 1 it is the same as x +4 = 0 It can be represented by { 4, 0} Sometimes the terms are used interchangably
Are there only 3 degree's in a polynomial equation?
No. A polynomial can have as many degrees as you like.
What is the polynomial degree of 4ab5 2ab-3a4b3?
To find the polynomial degree you have only to add the exponents of all of the different components of the polynomial. In your case, you would add 1 and 5 from 4ab5 to get 6, 1 and 1 from 2ab to get 2, and 4 and 3 from 3a4b3 to get 7. Since the degree of the third component is the highest, that is you're answer.
What completes the number sequence 2 6 3 8 6 12?
No number completes it because the sequence can go on forever. There are infinitely many possible solutions: given any seventh number it is possible to find a polynomial of degree 6 that will fit the above six points and the selected seventh. There is only one polynomial of degree 5, and using that as the position to value rule, the next number is 131.
What number comes next in this sequence 1 3 11 47 239 give answer with explanation?
821. The explantion is that they can be generated by the polynomial below: the only polynomial of degree 4. There are infinitely many other possibilities and given any "next number" it is possible to find a polynomial of degree 5 that will generate the 5 given numbers and the specified "next". Un = (53n4 - 486n3 + 1627n2 - 2250n + 1068)/12 for n = 1, 2, 3, ...
What is the next number in the following series 9 4 10 11 6?
It is possible to find a polynomial of order 5 such that, using that polynomial for the position to term rule, ANY number can be the next number.However, the only polynomial of degree 4 that will fit the given points isUn = (15n4 - 214n3 + 1041n2 - 1970n + 1344)/24 for n = 1, 2, ...Using this rule, the next numbers are 9, 49, 170, ...
Is it possible to find the discriminant of a binomial?
A polynomial discriminant is defined in terms of the difference in the roots of the polynomial equation. Since a binomial has only one root, there is nothing to take its difference from and so in such a situation, the discriminant is a meaningless concept.
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).
What are the steps to solve these problems Find the degree of each polynomial 5a-2b2 plus 1 and 24xy-xy3 plus x2?
The degree of a polynomial function is the highest power any single term is raised to. For example, (5a - 2b^2) is a second degree function because the "b^2" is raised to the second power and the "a" is only raised to the (implied) first power. For (24xy-xy^3 + x^2) it is a third degree polynomial because the highest power is the cube of -xy.
Is it possible for a polynomial function of degree 3 to have no real zeros?
Yes - but only if the domain is restricted. Normally the domain is the whole of the real numbers and over that domain it must have at least one real zero.
The polynomial given below has rootss?
You forgot to copy the polynomial. However, the Fundamental Theorem of Algebra states that every polynomial has at least one root, if complex roots are allowed. If a polynomial has only real coefficients, and it it of odd degree, it will also have at least one real solution.
How do you find greatest common factor of a polynomial equation?
It is not possible to give a sensible answer to this question. The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers or polynomials. If you have only one number or polynomial there is nothing for it to have a factor in common with!
What is the next number in the sequence 2 3 6 7 1?
It can be any number you like. Given any number, it is always possible to find a polynomial of degree 5 that will fit the above numbers and the give sixth number. The only polynomial of order 4 is Un =(-n4 - 6n3 + 85n2 - 174n + 144)/24 for n = 1, 2, 3, ... This gives the next term as -18.
