Question

Use the x-intercept method to find all real solutions of the equation. x^3-8x^2+9x+18=0

Answer 1

Answer:

a. $x=-1,3,\:or\:6$

Step-by-step explanation:

The given equation is;

$x^3-8x^2+9x+18=0$

To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator or software.

The corresponding function is

$f(x)=x^3-8x^2+9x+18$

The solution to $x^3-8x^2+9x+18=0$ is where the graph touches the x-axis.

We can see from the graph  that; the x-intercepts are;

(-1,0),(3,0) and (6,0).

Therefore the real solutions are:

$x=-1,3,\:or\:6$

Answer 2

Answer:

Use a graphing utility or a graphing calculator.

x = -1, 3, 6.   (3 real solutions).

Step-by-step explanation:

The points of intersection on the x axis are the 3 solutions to the equation.