Use the rational zeros theorem to list all possible zeros of the function .
Enter the possible zeros separated by commas. You do not need to factor the polynomial.

Ask by Bob Campbell. in the United States

Jan 31,2025

Question

Use the rational zeros theorem to list all possible zeros of the function $$ f(x)=5 x^{3}-4 x^{2}-2 x+3 $$. Enter the possible zeros separated by commas. You do not need to factor the polynomial.

UpStudy AI · Accepted Answer

The possible rational zeros of the function $$ f(x) = 5x^3 - 4x^2 - 2x + 3 $$ can be determined using the Rational Zeros Theorem.

According to the theorem, any possible rational zero is of the form $$ \frac{p}{q} $$, where:
- $$ p $$ is a factor of the constant term (which is 3).
- $$ q $$ is a factor of the leading coefficient (which is 5).

**Factors of 3 (constant term):** ±1, ±3  
**Factors of 5 (leading coefficient):** ±1, ±5

Thus, the possible rational zeros are:
$$
\pm1, \pm3, \pm\frac{1}{5}, \pm\frac{3}{5}
$$

**Listing them out:**
$$
-3, -1, -\frac{3}{5}, -\frac{1}{5}, \frac{1}{5}, \frac{3}{5}, 1, 3
$$

**Answer:**
-3, -1, -3/5, -1/5, 1/5, 3/5, 1, 3
The possible rational zeros are: -3, -1, -3/5, -1/5, 1/5, 3/5, 1, 3.

Use the rational zeros theorem to list all possible zeros of the function .
Enter the possible zeros separated by commas. You do not need to factor the polynomial.

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Use the rational zeros theorem to list all possible zeros of the function . Enter the possible zeros separated by commas. You do not need to factor the polynomial.