# Rational roots, functions, modeling.

#### niyak

##### New member
OKAY I have a trg test make up and due tomroow and I have no clue what I am doing, ive searched online chatrooms and they all want money. so this is basiaclly my last hope the test is over rATIONAL ROOTS ZEROS POLYNOMIALS ETC. please show all work if answering
QUESTIONS i NEED HELP ON BELOW:
3. The revenue for a type of cell phone is given by the equation ; R(X) = -20x^2 +500x where x is the number of units sold.
a) what is the revunue if 20 units are sold?
b) what is the maximum revenue?
c)how many cell phones will maximize the revunue?

4.Describe the graphical implications of real zeros ( what happens on the graph when the function has real zeros)?
5. If a function were to have a degree of 5 , list the possibilities for combinations of real and imaginary zeros for the function.

List all possible rational roots for each polynomial and then find all roots.
you can use factoring ,substitution factoring, or synthetic division
f(x)=x^4-3x^3-3x^2+11x-6

f(x)=x^3-3x^2-3x+21

f(x)=x^4+3x^2-4

Given the zeros, find the least polynomial of the given degree.
9.A polynomial of degree 5 with zeros :2 multiplicity of 2,-3,0 multiplicity of 2

10. a polynomial of degree 4 with zeros :1,-4,3i

find the quadratic model for the given data on a number of hours watching tv per household per day since 1960 (t=0 for 1960)

year 1960,1972,1980,1985,1991,2000,2010
#of tvs .87, 1.8, 2.5, 2.6, 3.6, 3.5, 3.3
model_____________
predict the number of hours for 1999_______________
predict the numbers of hours for 2020________________

#### Jameson

Staff member
Re: Rational roots

Hi there. Are these questions for a take home test that is for a grade? If so, I'm sorry but we can't help you unless you can demonstrate that your teacher is ok with you receiving help. We will be glad to help you with these kinds of problems in the future but for a test is something we won't do. If I'm mistaken with this please let me know.

#### niyak

##### New member
Re: Rational roots

this isnt the test this is the review for the test I take tomorrow.

#### Jameson

Staff member
Re: Rational roots

3. a) R(x) will tell you the revenue for x units. What is R(20)?
b) This is a parabola that opens downward which means that the maximum point on the graph will be at at the vertex. Have you taken calculus? If not, do you know how to complete the square to get this into a more general form of $$\displaystyle f(x)=a(x-h)^2+k$$?
c) Once you solve b you can figure this out as well.

EDIT: Another way to find the vertex from the form you have $$\displaystyle f(x)=ax^2+bx+c$$ is that the x-coordinate of the vertex is $$\displaystyle \frac{-b}{2a}$$. Have you seen this before?

#### CaptainBlack

##### Well-known member
Re: Rational roots

4.Describe the graphical implications of real zeros ( what happens on the graph when the function has real zeros)?
The graph cuts the x-axis, though it may only touch the x-axis if the root is a multiple root of even multiplicity.

CB

#### CaptainBlack

##### Well-known member
Re: Rational roots

5. If a function were to have a degree of 5 , list the possibilities for combinations of real and imaginary zeros for the function.
A polynomial function of degree 5 with real coefficients can have 1, 3 or 5 real roots (counting multiplicities, so it must have at least one real root). For a polynomial with real coefficients the complex roots occur in conjugate pairs and so there must be an even number of them (which is why the number of real roots must be odd for a degree 5 polynomial).

List all possible rational roots for each polynomial and then find all roots.
you can use factoring ,substitution factoring, or synthetic division

f(x)=x^4-3x^3-3x^2+11x-6

f(x)=x^3-3x^2-3x+21

f(x)=x^4+3x^2-4
For this part you need to use the rational root theorem, which states that a rational root of a polynomial with integer coefficients must be of the form of the ratio of a factor of the constant term to a factor of the coefficient of the highest degree term. In all these cases the latter is 1, so you need to test all the factors of the constant term to see if they are roots.

For the first the list of potential roots is: +/-1, +/-2, +/-3, +/-6.

CB