Question

Finding the Zeros

Answer 1

Regarding #6:

You did well in identifying the possible rational roots.  Like you, I checked out x=3 as a possible root.  The 3 coefficients remaining after that are 1, -4 and 2.

They correspond to the quadratic expression 1x^2 -4x + 2.

We can apply the quadratic formula here.  a=1, b=-4 and c=2.

                  -(-4) plus or minus sqrt( [-4]^2 - 4(1)(2)  )
Then x = ------------------------------------------------------------
                                              2(1)
              4 plus or minus sqrt(8)           4 plus or minus 2sqrt(2)
or  x = -----------------------------------  =  -----------------------------------
                            2                                                   2

Then x = 2 plus or minus sqrt(2).

If you wanted, you could check your work here by using synthetic division.  Let the divisor be 2+sqrt(2) and the 3 coefficients    be   1   -4   2.

The remainder should be zero.

Answer 2

Use the quadratic formula to solve the equations . you will get the answers