Find all zeros. One factor has been given
7)

Ask by Barker Henry. in the United States

Mar 31,2025

Question

Find all zeros. One factor has been given 7) $$ f(x)=3 x^{3}+4 x^{2}-17 x-6 ; x+3 $$

UpStudy AI · Accepted Answer

Solve the equation $$ 3x^{3}+4x^{2}-17x-6=0 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$3x^{3}+4x^{2}-17x-6=0$$
- step1: Factor the expression:
  $$\left(x-2ight)\left(x+3ight)\left(3x+1ight)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&x-2=0\&x+3=0\&3x+1=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=2\&x=-3\&x=-\frac{1}{3}\end{align}$$
- step4: Rewrite:
  $$x_{1}=-3,x_{2}=-\frac{1}{3},x_{3}=2$$
The zeros of the function $$ f(x) = 3x^{3} + 4x^{2} - 17x - 6 $$ are $$ x = -3, x = -\frac{1}{3}, x = 2 $$.
The zeros of the function are $$ x = -3 $$, $$ x = -\frac{1}{3} $$, and $$ x = 2 $$.

Find all zeros. One factor has been given
7)

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