Answer:
f(x) = x² - 10x + 27
Step-by-step explanation:
Given the x- intercepts of f(x) are x = a and x = b, then the factors are
(x - a) and (x - b) and f(x) is the product of the factors, that is
f(x) = (x - a)(x - b)
Here the x- intercepts are 5 - i[tex]\sqrt{2}[/tex] and 5 + i[tex]\sqrt{2}[/tex] , thus the factors are
(x - (5 - i[tex]\sqrt{2}[/tex] )) and (x - (5 + i[tex]\sqrt{2}[/tex] )) , that is
(x - 5 + i[tex]\sqrt{2}[/tex]) and (x - 5 - i[tex]\sqrt{2}[/tex] , then
f(x) = (x - 5 + i[tex]\sqrt{2}[/tex] )(x - 5 - i[tex]\sqrt{2}[/tex] ) ← expand using FOIL
= (x - 5)² - 2i² ← i² = - 1
= x² - 10x + 25 + 2
= x² - 10x + 27
