What are the roots of the polynomial equation? $$ \begin{array}{l}\frac{1}{2} x(x-7)(x+9)=0 \ ext { Select each correct answer. } \ \square=\frac{1}{2} \ \square \ \square\end{array} $$ $$ \square \frac{1}{2} $$ $$ \square $$

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What are the roots of the polynomial equation? $$ \begin{array}{l}\frac{1}{2} x(x-7)(x+9)=0 \ 	ext { Select each correct answer. } \ \square=\frac{1}{2} \ \square \ \square\end{array} $$ $$ \square \frac{1}{2} $$ $$ \square $$

UpStudy AI · Accepted Answer

To find the roots of the polynomial equation:

$$
\frac{1}{2} x (x - 7) (x + 9) = 0
$$

we set each factor equal to zero and solve for $$ x $$:

1. **First Factor:**
   $$
   \frac{1}{2} = 0
   $$
   This equation has **no solution** since $$\frac{1}{2}$$ is a constant and never equals zero.

2. **Second Factor:**
   $$
   x = 0
   $$
   **Root:** $$ x = 0 $$

3. **Third Factor:**
   $$
   x - 7 = 0 \quad \Rightarrow \quad x = 7
   $$
   **Root:** $$ x = 7 $$

4. **Fourth Factor:**
   $$
   x + 9 = 0 \quad \Rightarrow \quad x = -9
   $$
   **Root:** $$ x = -9 $$

**Summary of Roots:**
- $$ x = 0 $$
- $$ x = 7 $$
- $$ x = -9 $$

These are the values of $$ x $$ that satisfy the original equation.
The roots of the equation are $$ x = 0 $$, $$ x = 7 $$, and $$ x = -9 $$.

What are the roots of the polynomial equation?

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