There are two ways to do this:

First way:  Let the roots be +r and -r

Then

x² - kx + 8 = 0

whould have to factor as

(x - r)(x + r) = 0

which multiplies out to

x² + rx - rx + r² = 0

          x² + r² = 0 

So since the terms in x cancel, the coefficient of r
must be zero, which makes k = 0.

However the roots are imaginary since r² must equal to 8

x² + 8 = 0

    x² = -8
           __ 
     x = ±Ö-8
             ___
     x = ± iÖ4*2
             _
     x = ±2iÖ2

------------------------

The other way to do it is to use the quadratic formula:


x² - kx + 8 = 0




               


The two roots are 

 and 

Setting one equal to the negative or the other:



Multiply through by 2





Subtracting the radical from both sides:

          k = -k

         2k = 0

          k = 0

And the two roots are















Edwin