Question

3 What is/are the z-intercepts of the graph y=-2³-52² - 3x + 9? OA (-3,0), (-1,0) O. B. (3.0), (1,0) OC. (3.0), (-1,0) O.D. (-3,0), (1,0) Reset Selection m

Answer 1

We will have the following:

We will determine the x-intercepts as follows:

$f(x)=-x^3-5x^2-3x+9$

Thus, the critical points will be given by:

$\begin{gathered} f^{\prime}(x)=-3x^2-10x-3=0\Rightarrow x=\frac{-(-10)\pm\sqrt{(-10)^2-4(-3)(-3)}}{2(-3)} \\ \\ \Rightarrow x=-3 \\ \\ and \\ \\ \Rightarrow x=1 \end{gathered}$

Now, we have that the x-intercepts are located at:

$\begin{gathered} (-3,0) \\ \\ and \\ \\ (1,0) \end{gathered}$