g(x) = x² - [tex]\frac{13}{2}[/tex] x + 3 is a possible polynomial
given x -intercepts x = a and x = b, then
(x - a) and (x - b) are the factors and g(x) is the product of the factors
here x = [tex]\frac{1}{2}[/tex] and x = 6 are the x-intercepts, hence
(x - [tex]\frac{1}{2}[/tex]) and (x - 6) are the factors
g(x) = (x - [tex]\frac{1}{2}[/tex])(x - 6)
= x² - [tex]\frac{13}{2}[/tex] x + 3
