"Explain why the facts given are contradictory; f is a polynomial function of degree 4 whose coefficients are real numbers; two of its zeros are - 3 and 4 - i. Explain why one of the remaining zeros must be a real number. Write down one of the missing zeros.

Q: What type of polynomial satisfies f"(x)=0 for all x?

A: Topic-polynomial

Q: Describe how to use Descartes’s Rule of Signs to determine the possible number of positive real…

A: Descartes' Rule of Sign – It is used to determine the number of real zeros of any given polynomial…

Q: Consider the polynomial function f(x) = x - 3x3 + 3x? whose domain is (-0, 0). Find the following:

A: d) The given function  fx=x4-3x3+3x2 Differentiate with respect to x f'x=4x3-9x2+6x       =x4x2-9x+6…

Q: It is possible for a third-degree polynomial function with integer coefficients to have no real…

A: To find whether the statement is true or false  Given, a polynomial of degree 3 with integer…

Q: Three of the zeros of a fourth-degree polynomial function f are -3, 4, and -5i. What is the other…

A:

Q: If a third degree polynomial has a lone x-intercept at x a , discuss what this implies about the…

A:

Q: Find the upper and the lower bound of the zeroes of each polynomial function. Given Upper bound…

A: As per our guidelines we are supposed to solve only three sub part of the problem. For the solution…

Q: When a polynomial function f is divided by x - c, theremainder is_______

A: Give a polynomial function f is divided by x - c

Q: Determine whether the following statement is true or false. If false, explain why. A polynomial…

A:

Q: What is a polynomialfunction in degree 1

A:

Q: Construct a polynomial function with the following properties: fifth degree, 3 is a zero of…

A: Given information :- Construct a polynomial function with the following properties fifth degree, 3…

Q: What is a polynomial function?

A: To Explain: what is a polynomial function

Q: If r is a solution to the equation f(x)=0               , name three additional statements that can…

A:

Q: Find an nth-degree polynomial function with real coefficients satisfying the given conditions, n =…

A: Given: n=4;  means the polynomial's maximum power will be 4zeroes:−2, −12 and if(1)=18

Q: Construct a polynomial function with the following properties: fifth degree, 4 is a zero of…

A: Let the polynomial be p(x). Now as 4 is a zero of p(x) of multiplicity 2, so (x-4)² is a factor of…

Q: Each polynomial function has exactly one positive zero.Approximate the zero correct to two decimal…

A: Given polynomial function          f(x)=3x4+4x3-8x-2

Q: Use the given information provided below to write an equation of a polynomial function with:…

A:

Q: Explain why a polynomial with real coefficients of degree 3 must have at least one real zero.

A: Given, A 3rd degree polynomial with real coefficients. Since the given polynomial is of degree 3,…

Q: Why is it not a polynomial function

A: A Polynomial function is expressed in the form of P(x)=anxn+an-1xn-1+an-2xn-2+...+a2x2+a1x+a0And the…

Q: 8. Find one zero of the polynomial f(x)=2x-x-6x+3 %3D

A: Given function is: Apply rational root theorem to get roots of polynomial. If the polynomial has a…

Q: What are the zeros of a polynomial function and how are they found?

A: Let f(x)=anxn+an-1xn-1+⋯+a3x3+a2x2+a1x+a0  be a polynomial of degree n. A root or a zero of a…

Q: Explain why the facts given are contradictory.; f is a polynomial function of degree 3 whose…

A: f is a polynomial function of degree 3 whose coefficients are real numbers; its zeros are 2, i, and…

Q: What is the polynomial, in factored form, for the function with the leading coefficient 6, and zeros…

A:

Q: Construct a polynomial function with the following properties: third degree, 4 is a zero of…

A: Given information: Third degree, 4 is a zero of multiplicity 2, -1 is the only other zero, leading…

Q: Sketch a higher degree polynomial with the following roots: -2, 3, -3, 6. f(x) 9,

A: It is given that the roots are -2, 3, -3 and 6. That is, x+2=0, x-3=0, x+3=0 and x-6=0. The…

Q: If f is a polynomial function, and f(a) and f(b) have opposite signs, what must occur between a and…

A: Since f is a polynomial, so it is a continuous function.

Q: Write a polynomial f (x) that satisfies the given conditions. 9 Degree 3 polynomial with integer…

A: Complex roots occurs in conjugate pairs

Q: Find a polynomial f(x) of degree 5 that has the following zeros. 5 (multiplicity 2), 0,-3, -8 Leave…

A:

Q: Based on your answers to the previous problem, draw a sketch of the polynomial f (x) = -2(x+4)* (x+…

A: The given polynomial function: fx=-2x+43x+2x-32

Q: 8. Determine algebraically the polynomial function that passes through the points below.

A: Given,

Q: Construct a polynomial function with the following properties: fifth degree, 4 is a zero of…

A:

Q: what could be a polynomial with a degree of 5 if its zeros are -2,1, and 4?

A: The given zeros are, –2, 1 and 4.

Q: Explain why a polynomial function of degree 20 cannot cross the x-axis exactly once?

A: Explain why a polynomial function of degree 20 cannot cross the x-axis exactly once?

Q: How many turns would be there in the polynomial function of degree 3?

A: Concept: Various graph of diffrent polynomials is explained below:

Q: Construct a polynomial function with the following properties: fifth degree, 2 is a zero of…

A:

Q: What is the polynomial function of least degree whose only zeros are -3,-2, and 4? Drag a value to…

A: Here we find the polynomial function of least degree whose only zeros are -3,-2 and 4

Q: Find the quadratic polynomial whose graph goes through the points (-1, 3), (0, 1), and (1,7). f(x) =

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Q: Write a polynomial function with the roots/zeros: 0 (with multiplicity 3), -1/2, 3/4, 7i√2, and…

A:

Q: write a polynomial f(x) that meets the given conditions. answers my vary. degree 3 polynomial with…

A: Given that 1, 7 and 6 are zeros of f(x).Then (x -1), (x - 7) and (x – 6) are factors of…

Q: Construct a polynomial function with the following properties: fifth degree, 2 is a zero of…

A:

Q: Find a polynomial f (x) of degree 4 that has the following zeros. 0,-2, -6, 5 Leave your answer in…

A: Using the fact that if r is a root then x-r is a factor of the polynomial

Q: Use the given polynomial function to answer the questions. f (x) = x² (2x – 1)² - What is the degree…

A:

Q: I’ve noticed that f(-x) is used to explore the number of negative real zeros of a polynomial…

A: A function f(x) is said to be an even function of x if f(-x) = f(x). A function f(x) is said to be…

Q: If f is a polynomial function, and f(a) and f(b) have opposite signs, what must occur between a and…

A: If we consider geometric interpretation of f, then it be more easier. (I)   As f(a) and f(b) have…

Q: Construct a polynomial function with the following properties: fifth degree, 4 is a zero of…

A:

Q: What is the equation of this degree 6 polynomial function?

A:

Q: What is a cubic polynomial function in standard form with zeros -4, -5, and 4?

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.