Suppose that R(x) is a polynomial of degree 7 whose coefficients are real numbers.
Also, suppose that R(x) has the following zeros.
−4 −4i, 2i

Answer the following.
(a) Find another zero of R(x).

(b) What is the maximum number of real zeros that R(x) can have?

(c) What is the maximum number of non-real zeros that R(x) can have?

Respuesta :

so... it has degree of 7, so based on the fundamental theorem of algebra....it can have at most 7 solutions

now.. you have −4, −4i, 2i  <--- there are two complex ones there

-4i or 0-4i  and 2i or 0+2i

now.. bear in mind that, complex solutions never come all by their lonesome, they come with their sister, the conjugate

thus, that means 0-4i comes with 0+4i and 0+2i comes with 0-2i

that makes only 5 roots though

that simply means that, the -4 one, has a multiplicity of 3

as far as the B) and C) sections, check Descartes Rule of Signs
which surely you've covered already

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division

R(x) = −4 −4i, 2i

What is a polynomial with example?

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer.

For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.

To learn more about polynomial, refer

https://brainly.com/question/20911331

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