Find a polynomial of degree THREE with zeros 0 and i

In summary, the conversation discusses various questions related to finding the domain of a function, finding an equation of a line passing through a given point and perpendicular to a given line, finding a polynomial with given zeros, and solving a system of equations. The speaker encourages the listener to understand the precise definitions of key terms before attempting to solve the problems. The conversation also mentions that the problems are for a college algebra class and suggests using the index of the textbook for help.
  • #1
lauren6568
2
0
any know how to do these:

the domain of the function F(x)=1 over 1-x is...

find an equation of a line passing through (-4,-5) and perpendicular to the line 2x + y = -4

find a polynomial of degree THREE with zeros 0 and i

the system of equations x+3y-z=5
3x-y+z=-3
2x+y=1 how many solutions

[?] [?]
 
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  • #2
What class is this for?

Question 1:
Find the domain of
[tex]f(x)=\frac{1}{1-x}[/tex]

The domain is the set of all [tex]x[/tex] so that [tex]f(x)[/tex] exists. (Hint: what is [tex]\frac{1}{0}[/tex]?)

Question 2:
You'll need to use slope (or something similar) to do this problem.

Question 3:
Do you know what the zeros of a polynomial are, or what the degree of a polynomial is?

Question 4:
Can you find any solutions to the system of equations?
 
  • #3
its for college algebra...i'm doing my review for my exam and I have no clue how to do most of these problems
 
  • #4
So what are your ideas on question 1?

Do you know what 'domain' means?
 
  • #5
I have no clue how to do most of these problems

Do you mean that your textbook doesn't even define these terms? Does it have an index?

Most of the problems are just applications of the index. You can't find the domain of a function if you don't know (precisely) what "domain" means!

Look up "domain", "slope", "polynomial" in the index of your book and read the definitions.

I'm not being sarcastic here (well, I'm trying really hard not to be!). Most beginning math students don't understand how important it is to know the precise definitions, not just have a "general idea" what something is.
 
  • #6
These are the foundation problems which is better to understand yourself than posting unless and until u have some problem grasping the concept
 

1. What does it mean to find a polynomial of degree THREE with zeros 0 and i?

Finding a polynomial of degree three with zeros 0 and i means finding a polynomial function that, when set equal to zero, will have solutions at 0 and i. In other words, the polynomial will have roots at 0 and i.

2. How do you find a polynomial of degree THREE with zeros 0 and i?

To find a polynomial of degree three with zeros 0 and i, you can use the fact that complex zeros come in conjugate pairs. This means that if i is a zero, then -i is also a zero. You can then use the fact that the product of the roots of a polynomial is equal to the constant term divided by the leading coefficient. By setting up and solving a system of equations using these facts, you can find the coefficients of the polynomial.

3. Can a polynomial of degree THREE have more than two complex zeros?

Yes, a polynomial of degree three can have more than two complex zeros. In fact, the Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n complex zeros, including repeated ones. This means that a polynomial of degree three can have three distinct complex zeros, or two distinct complex zeros and one repeated complex zero.

4. Is it possible for a polynomial of degree THREE with zeros 0 and i to have only real coefficients?

No, it is not possible for a polynomial of degree three with zeros 0 and i to have only real coefficients. Since i is a complex number, it cannot be represented with only real numbers. This means that at least one of the coefficients in the polynomial will have to be complex as well.

5. Can a polynomial of degree THREE with zeros 0 and i have a degree higher than three?

No, a polynomial of degree three with zeros 0 and i cannot have a degree higher than three. This is because the degree of a polynomial is equal to the highest power of the variable in the polynomial. Since a polynomial of degree three has a maximum power of three, it cannot have a higher degree.

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