37.4k views
3 votes
Find the zeros of the function: f(x) = 3x^3 - 4x^2 +8x+8

User PhistucK
by
8.0k points

1 Answer

4 votes
To find the zeros of the function f(x) = 3x^3 - 4x^2 +8x+8, we need to solve for x when f(x) = 0.

One way to do this is to use synthetic division. We'll start by trying x = 1 as a possible zero:

1 | 3 -4 8 8
| 3 -1 7
| -----------
| 3 -1 7 15

Since the remainder is not zero, x = 1 is not a zero of the function. Let's try x = -1:

-1 | 3 -4 8 8
| -3 7 -15
| -----------
| 3 -7 15 -7

Since the remainder is zero, x = -1 is a zero of the function. We can now factor out (x + 1) from the polynomial using long division or synthetic division:

(x + 1)(3x^2 - 7x + 7)

The remaining quadratic factor does not have any real zeros, so the zeros of the function f(x) are:

x = -1 (with a multiplicity of 1)
User Yifu Yan
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories