Pre Calculus Please Explain

Question

What is the minimal degree of the polynomial function with partial solution set x={1 mult 3, -4√3}?

Answer 1

If 1 is a root with multiplicity 3, then (x-1)³ is part of the factored form of the polynomial.

If -4√3 is a root then 4√3 is also a root (if we assume that the polynomial has integer coefficients). So, we would then have (x - 4√3) and (x + 4√3) as factors.

So, (x - 1)³ (x - 4√3)(x + 4√3) is a polynomial of minimal possible degree with degree 5.