Question

If a polynomial function f(x) has roots 3 + sqrt5 and -6, what must be a factor of f(x)?

Answer 1

If a is a factor of f(x)

Then

• (x-a)=0

So if a=3+√5 and -6

The expression is

• (x-(3-√5))(x-(3+√5))(x+6)=0

Option B

Answer 2

• (x - (3 - √5))

Explanation:

If there are roots:

• 3 + √5 and - 6, then another root should be 3 - √5

So we would have factors of:

• f(x) = (x - (3 - √5))(x - (3 + √5))(x + 6)

Correct choice including the third factor is B