Thread: help with polynomial roots question

Use synthetic division to show that all of the real zeros of f(x)=x^3-3x^2-4x+5 lie in the interval [-2,4]

Hello, cityismine!

Use synthetic division to show that all of the real zeros of
lie in the interval

I'm not sure why Synthetic Divison is used here . . .

We find that: .
. . The graph is below the x-axis.

We find that: .
. . The graph is above the x-axis.

We find that: .
. . The graph is below the x-axis.

We find that:.
. . The graph is above the x-axis.

So far, the graph looks like this:

Code:

            |
            |         (4,5)
       (0,5)*           *
            |           :
     -2     |     2     :
    --+-----+-----+-----+----
      :     |     :     4
      :     |     :
      :     |     :
      *     |     *
   (-2,-7)  |   (2,-7}
            |

Since a polynomial function is continuous, the graph must cross the x-axis
. . on the intervals
And those are the three (real) zeros of the cubic function.

Code:

            |
            *           *
          * | *         :
     -2     |     2     :
    --+--o--+--o--+---o-+----
      :     |     :     4
      :     |     :  *
      : *   |   * : *
      *     |     *
            |