Answer:
x² - 3x + 0.25 = 0
Step-by-step explanation:
Given a root x = a then the corresponding factor is (x - a)
Given roots x = 1.5 + [tex]\sqrt{2}[/tex] and x = 1.5 - [tex]\sqrt{2}[/tex] then the factors are
(x - (1.5 + [tex]\sqrt{2}[/tex] ) ) and (x - (1.5 - [tex]\sqrt{2}[/tex] ) ) , that is
(x - 1.5 - [tex]\sqrt{2}[/tex] ) and (x - 1.5 + [tex]\sqrt{2}[/tex] )
The equation is then the product of the factors
(x - 1.5 - [tex]\sqrt{2}[/tex] )(x - 1.5 + [tex]\sqrt{2}[/tex] ) = 0 ← expand factors using FOIL
(x - 1.5)² - ([tex]\sqrt{2}[/tex] )² = 0
x² - 3x + 2.25 - 2 = 0
x² - 3x + 0.25 = 0
