# Thread: Seeking Math help +rep pre cal questions

1. ## Seeking Math help +rep pre cal questions

1. Translate the statement below to an equation using absolute value and solve:
The distance between 50 and me is at least 10.

2. Using the given zero, find all of the zeros and write a linear factorization of f(x).

1+3i is a zero of f(x)=x^4-2x^3+5x^2+10x-50

2. 1. Translate the statement below to an equation using absolute value and solve:
The distance between 50 and me is at least 10.

|x-50| ≥ 10

3. No problem. I don't remember how to do #2 though D:

---------- Post added at 03:32 PM ---------- Previous post was at 03:23 PM ----------

http://www.wolframalpha.com/input/?i...x%5E2%2B10x-50

4. ## The Following User Says Thank You to Carrot For This Useful Post:

John (01-31-2012)

5. 1+3i is a zero of f(x)=x^4-2x^3+5x^2+10x-50
Since 1+3i is a root, 1-3i is also a root. ((x-1)-3i)((x-1)+3i)=(x-1)^2-(3i)^2=x^2-2x+1-9i^2=x^2-2x+10
Use long division to get x^2-5.
Find the two roots of that are +- radical 5.
Linear factorization is f(x)=(x-1-3i)(x-1+3i)(x+5^.5)(x-5^.5)

6. Originally Posted by bamag
1+3i is a zero of f(x)=x^4-2x^3+5x^2+10x-50
Since 1+3i is a root, 1-3i is also a root. ((x-1)-3i)((x-1)+3i)=(x-1)^2-(3i)^2=x^2-2x+1-9i^2=x^2-2x+10
Use long division to get x^2-5.
Find the two roots of that are +- radical 5.
Linear factorization is f(x)=(x-1-3i)(x-1+3i)(x+5^.5)(x-5^.5)

it is cool, but you may give the explanation that why 1-3i is also a root.

you may add [since all coefficient are real number, therefore (a+bi)(1+3i)=constant +0i,hence a=1,b=3 ]

7. Originally Posted by dodowong303
it is cool, but you may give the explanation that why 1-3i is also a root.

you may add [since all coefficient are real number, therefore (a+bi)(1+3i)=constant +0i,hence a=1,b=3 ]
It is simply the conjugate roots theorem. If a+bi is a root, then a-bi is also a root, and vise versa.

8. Originally Posted by bamag
It is simply the conjugate roots theorem. If a+bi is a root, then a-bi is also a root, and vise versa.
i know but my teacher will deduct marks form missing some stupid simple explanation such as a+bi&a-bi must be pair,etc.......==

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