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

To find the roots of the polynomial equation \(\frac{1}{2} x(x-7)(x+9)=0\), we can set each factor equal to zero. The first factor is \(x = 0\). The second is \(x - 7 = 0\), which gives \(x = 7\). The third factor, \(x + 9 = 0\), provides \(x = -9\). Therefore, the roots are \(x = 0\), \(x = 7\), and \(x = -9\). Now, let’s consider those roots in terms of their graphical representation! Just imagine plotting these on a graph: you’d see the polynomial curve intersecting the x-axis at three distinct points. At \(x = 0\), the curve touches the axis and bounces back. When it hits \(x = 7\), it crosses the axis, going up into positive territory, and at \(x = -9\), it dips down before rising again. This visual representation helps in understanding polynomial behavior!