SOLUTION: I am having the most difficult time figuring out how to format this into a polynomial. I know the highest exponent degree must be at 4, and that it also must include x^2 but that i

Question 1045791: I am having the most difficult time figuring out how to format this into a polynomial. I know the highest exponent degree must be at 4, and that it also must include x^2 but that is all I can figure out. Any help would be much appreciated.

Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; Zeros -5+5i; 1 multiplicity 2
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Degree four means you will have something like and the zeros are a, b, c, and d.

You are given two of the zeros, and one of them is repeated (multiplicity of 2).
for some not yet finished value c.

To determine your last binomial factor, you must understand that Complex zeros occur in conjugate pair. This means, .

Now your polynomial IN FACTORED FORM is .

Now simplify and arrange the polynomial into general form.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the equation is degree 4.
therefore you should have 4 roots.
the highest exponent will be 4.

let's look at what you have:

you are asked to Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; Zeros -5+5i; 1 multiplicity 2

your roots are, or should have been given as:

x = 5 plus or minus 5i,
x = 1 with a multiplicity of 2.

complex roots always come in pairs.

if a + bi is a root, then a - bi is also a root.

to find the factors, your set x equal to the root and then set the equation equal to 0.

for example:

x = 1 is set to 0 by doing the following:
subtract 1 from both sides of the equation to get x - 1 = 0
x - 1 is a factor.

they told you the root has a multiplicity of 2, therefore 2 of your factors are (x-1) * (x-1) which can also be written as (x-1)^2.

your complex roots come in pairs.

they should be 5 + 5i and 5 - 51.

set x = 5 + 5i
subtract 5 + 5i from both sides of the equation to get:
x - 5 - 5i = 0
that's one of the complex factors.

set x = 5 - 5i
subtract 5 from both sides of the equation and add 5i to both sides of the equation to get:
x - 5 + 5i = 0
that's the other of the complex factors.

your factors are (x-1)^2 * (x - 5 - 5i) * (x - 5 + 5i)

your equation will be:

(x-1)^2 * (x - 5 - 5i) * (x - 5 + 5i) = 0

multiply these factors out to get your equation.

(x - 5 - 5i) * (x = 5 + 5i) results in x^2 - 10x + 50

(x-1)^2 results in x^2 - 2x + 1

your equation would be:

(x^2 - 10x + 50) * (x^2 - 2x + 1) = 0

the result of that would be:

x^4 - 12x^3 + 71x^2 - 110x + 50 = 0

the general equation is y = x^4 - 12x^3 + 71x^2 -110x + 50.

to factor that equation, you set y = 0 to get what we had before as:

x^4 - 12x^3 + 71x^2 - 110x + 50 = 0

now it's in standard form for factoring.

RELATED QUESTIONS
Determine the required value of the missing probability to make the distribution a... (answered by robertb)
I am having a hard time with my Algebra One class. I know this is a bad example of a... (answered by askmemath)
I have done all the margin exercises and practice and I am still having a very difficult... (answered by Alan3354)
Hi, I am having trouble figuring out how to find the real and imaginary zeros of... (answered by Alan3354)
Can someone help me with this, I am having a difficult time understanding how to plot the (answered by Alan3354)
Figuring out graphing of this polynomial: f(x) = 12x^3 - 12x^2 - 24x what I have... (answered by josgarithmetic)
Can someone please help me to understand the below problem. I am working with mutliplying (answered by scott8148)
I am having a difficult time figuring out what to do with the X+4000 in this problem, any (answered by JulietG)
Hello, I'm having a difficult time figuring out this word problem. It states (ONE number... (answered by ikleyn)