Question

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

Answer 1

Use a graphing utility or a graphing calculator.

x = -1, 3, 6. (3 real solutions).

Explanation:

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

Answer 2

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

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`