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Write a polynomial degree with real coefficients whose zeros include 13 plus i and 2 Write the polynomial degree in standard form?
To have a zero at 2, you need to include a factor (x - 2). To have a zero at 13 + i, you need a factor (x - (13 + i)). To have real coefficients, for each non-real factor you need to include its complex conjugate, so in this case, (x + 13 + i).Thus, you have the factors:
(x - 2)(x - (13 + i))(x + 13 + i)
You can multiply the factors together to get the polynomial into standard form. I suggest you start with the complex conjugates, that makes it easier.
What else can I help you with?
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.)
What is the standard form for a polynomial?
The standard form of a polynomial of degree n is anxn + an-1xn-1 + ... + a1x + a0 where the ai are constants.
What degree of polynomial will be produced by multiplying a third degree polynomial and a fourth degree polynomial?
seventh degree polynomial x3 times x4 = x7
What type of polynomial is formed by adding a second degree binomial to a fourth degree monomial. State the degree of this polynomial?
A fourth degree polynomial.
What is this polynomial's degree?
The degree of a polynomial is the highest power of the variable.
Is a polynomial of degree 0 is a constant term?
Yes, a polynomial of degree 0 is a constant term. In mathematical terms, a polynomial is defined as a sum of terms consisting of a variable raised to a non-negative integer power multiplied by coefficients. Since a degree 0 polynomial has no variable component, it is simply a constant value.
If you are asked to write a polynomial function of least degree with real coefficients and with zeros of 2 and i square roots of seven what would be the degree of the polynomial also wright equation?
3y2-5xyz yay i figured it out!!!!
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.)
What is the standard form for a polynomial?
The standard form of a polynomial of degree n is anxn + an-1xn-1 + ... + a1x + a0 where the ai are constants.
What are the solutions of a six-degree polynomial?
It depends on the polynomial and your degree of sophistication. In the complex domain, it will have six solutions, although not all of them need be different. If the coefficients are all real, then it will have 0, 2, 4 or 6 real solutions in the real domain.
How do you rewrite an polynomial and standard form?
A polynomial, of degree n, in standard form is:anxn + an-1xn-1 + ... + a1x+ a0 = 0 where n is an integer and the ai are constants.The answer about how to rewrite a polynomial depends on the form that it is given in.A polynomial, of degree n, in standard form is:anxn + an-1xn-1 + ... + a1x+ a0 = 0 where n is an integer and the ai are constants.The answer about how to rewrite a polynomial depends on the form that it is given in.A polynomial, of degree n, in standard form is:anxn + an-1xn-1 + ... + a1x+ a0 = 0 where n is an integer and the ai are constants.The answer about how to rewrite a polynomial depends on the form that it is given in.A polynomial, of degree n, in standard form is:anxn + an-1xn-1 + ... + a1x+ a0 = 0 where n is an integer and the ai are constants.The answer about how to rewrite a polynomial depends on the form that it is given in.
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.
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.
What degree of polynomial will be produced by multiplying a third degree polynomial and a fourth degree polynomial?
seventh degree polynomial x3 times x4 = x7
How many real roots can a fourth degree polynomial have?
Upto 4. If the coefficients are all real, then it can have only 0, 2 or 4 real roots.
A quadratic polynomial is a third-degree polynomial?
No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).
What type of polynomial is formed by adding a second degree binomial to a fourth degree monomial. State the degree of this polynomial?
A fourth degree polynomial.
