Use the boundedness theorem

Question

Use the boundedness theorem to show that f(x)=x^5-2x^3-x+2 has no real zero less than -3 and no real zero greater than 3

Answer 1

x^5-2x^3-x+2

  -3| 1    0  -2     0    -1      2

            -3   9  -21   63  -186

        1  -3   7  -21   62  -184   last row is alternating in sign so no zeroes less than -3

 

   3|| 1   0   -2    0   -1      2

             3     9  21  63   186

        1   3     7  21  62   188    last row all positive so no zeroes greater than +3

 

PLEASE  DON'T FORGET THE ZEROES FOR THE MISSING POWERS X⁴ AND X²