Answer:
x² - 6x + 6 = 0
Step-by-step explanation:
Given the roots are x = 3 - [tex]\sqrt{3}[/tex] and x = 3 + [tex]\sqrt{3}[/tex] , then the corresponding factors are
(x - (3 - [tex]\sqrt{3}[/tex] ) ) and (x - (3 + [tex]\sqrt{3}[/tex] ) ), that is
(x - 3 + [tex]\sqrt{3}[/tex] ) and (x - 3 - [tex]\sqrt{3}[/tex] )
The equation is then the product of the factors
(x - 3 + [tex]\sqrt{3}[/tex] )(x - 3 - [tex]\sqrt{3}[/tex] ) = 0
(x - 3)² - ([tex]\sqrt{3}[/tex] )² = 0
x² - 6x + 9 - 3 = 0
x² - 6x + 6 = 0
