Answer:
f(x) = x³ -4x² -5x +20
Step-by-step explanation:
If the function is to have rational coefficients, each complex or irrational square root must have a matching conjugate. That is, both -√5 and +√5 must be roots. If there is a root p, then there is a factor (x -p). The factored form of the minimal polynomial is ...
f(x) = (x -4)(x +√5)(x -√5)
= (x -4)(x² -5)
f(x) = x³ -4x² -5x +20
