Answer:
see explanation
Step-by-step explanation:
Given that x = [tex]\frac{3}{2}[/tex] and x = 4 are roots, then
(x - [tex]\frac{3}{2}[/tex]) and (x - 4) are factors
The quadratic is the product of it's factors, thus
(x - [tex]\frac{3}{2}[/tex])(x - 4) = 0 ← expand using Foil
x² - [tex]\frac{11}{2}[/tex] x + 6 = 0, or
2x² - 11x + 12 = 0 ( multiplying through by 2 )
