Help with arithmetic sequence problem

In summary, the zeros of the polynomial f(x) = x^3 - 33x^2 + 354x + k form an arithmetic sequence and the value of k can be determined by multiplying the factors (x-a)(x-b)(x-2b+a) and equating the coefficients.
  • #1
demonelite123
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The zeros of the polynomial f(x) = x^3 - 33x^2 + 354x + k form an arithmetic sequence. What is the value of k?

so i let the zeros = a, b, and c. then i did b - a = c - b since it's an arithmetic sequence and they have common differences. so now i have a + c = 2b. i don't know what to do from here. help is much appreciated!
 
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  • #2
Maybe you want four equations because you have four unknowns; although maybe you really have three unknowns (a, b, and k, since you determined c=(2b-a) ).

(x - a)(x - b)(x - (2b-a)) = x^3 - 33x^2 + 354x + k = 0

Could you use this, multiply the lefthand side, and then equate the coefficients?
 
  • #3
oh i see.
it took a while to multiply out the expression, but i got the answer.
thanks! :)
 

Related to Help with arithmetic sequence problem

1. What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference and is denoted by the letter d.

2. How do I find the common difference in an arithmetic sequence?

To find the common difference in an arithmetic sequence, you can subtract any term from the term that comes after it. This will give you the constant difference between the two terms. Alternatively, you can also use the formula d = (an - an-1), where d is the common difference, an is the nth term, and an-1 is the term before it.

3. Can you provide an example of an arithmetic sequence?

Yes, an example of an arithmetic sequence is 2, 6, 10, 14, 18, ... In this sequence, the common difference is 4, as each term is 4 more than the previous term.

4. How do I find the nth term in an arithmetic sequence?

The formula for finding the nth term in an arithmetic sequence is an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference. Simply plug in the values for a1 and d, and solve for an.

5. Can an arithmetic sequence have a negative common difference?

Yes, an arithmetic sequence can have a negative common difference. This means that each term will be subtracted by the same amount to get to the next term. For example, in the sequence 10, 6, 2, -2, -6, ..., the common difference is -4.

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