Question

Find the zeros of the polynomial function n(x) = −0..5x3−1.5x2+2x
, given its graph. Enter the zeros in order from least to greatest.

(1 point)
Responses

1, 0, -4
1, 0, -4

-4, 0, 1
-4, 0, 1

-1, 0, 4
-1, 0, 4

4, 0, -1

Answer 1

To find the zeros of the polynomial function \( n(x) = -0.5x^3 - 1.5x^2 + 2x \), we need to factor the polynomial and solve for \( n(x) = 0 \).

Let's first factor out the common term:

\[
n(x) = -0.5x^3 - 1.5x^2 + 2x = x(-0.5x^2 - 1.5x + 2)
\]

Now, we can find the zeros:

1. The first zero is from \( x = 0 \).
2. To find the other zeros, we need to solve \( -0.5x^2 - 1.5x + 2 = 0 \).

Multiplying through by -2 to eliminate the fraction:

\[
x^2 + 3x - 4 = 0
\]

Now we can factor this quadratic:

\[
(x + 4)(x - 1) = 0
\]

Setting each factor to zero gives us:

\[
x + 4 = 0 \quad \Rightarrow \quad x = -4
\]
\[
x - 1 = 0 \quad \Rightarrow \quad x = 1
\]

Therefore, the zeros of the polynomial are \( -4, 0, 1 \).

Listing them in order from least to greatest gives:

\[
-4, 0, 1
\]

So the correct response is:

**-4, 0, 1**