Answer: k = √6
Explanation: We have the equation:
(1/3)x^2 - 2
and we want to write this in the form:
(1/3)(x - k)(x +k)
k and -k are the solutions of the equation:
(1/3)x^2 - 2 = 0
wich are
[tex]+/- k = \frac{+/-\sqrt{-4*1/3*-2} }{2/3} = 3\frac{+/-\sqrt{8/3} }{2} = +/-3*\sqrt{2/3} = +/-\sqrt{6}[/tex]
so k = [tex]\sqrt{6}[/tex]
and we can write the equation as:
(1/3)(x - √6)(x +√6)
