Question

If a polynomial function f(x) has roots 3+ V5 and -6, what must be a factor of f(x)?

(X+(3-root5)
(X-(3-root5))
(X+(5+root3))
(X-(5-root3))

Answer 1

Explanation:

Radicals and imaginary numbers ALWAYS come in pairs when it comes to factors of polynomials. This is the called the conjugate theorem. If we are given a solution/root/zero that is

x = 3 + √5, then its conjugate is x = 3 - √5. Going backwards from the solution to the factor, we utilize the Zero Product Property and get

(x - (3 - √5)) which simplifies to (x - 3 + √5). if you are looking for the conjugate of the given zero, the choice you want is the second one down.