Question

If a polynomial function f(x) has roots 3+Sqrt(5) and -6, what must be a factor of f(x)

Answer 1

B

Explanation:

(x – (3-
`√(x) 5` ))

Answer 2

The two factors of the given polynomial f(x) are (x - 3 -√5) and (x +6) .

Explanation:

Here, the roots of the given polynomial f(x) are

Root 1 = 3 + √5

and Root 2 = (-6)

Now,as we know that if x = a is the root of the any given polynomial p(x), then the expression (x-a) is the FACTOR of the polynomial p(x).

Now, here root 1 : x = 3 + √5

So, x - (3 + √5 ) is the FACTOR of the f(x)

or, ( x - 3 -√5) is the first factor of f(x).

Also, here root 2 : x = (-6)

So, x - (-6 ) = x + 6 is the FACTOR of the f(x)

or, ( x +6 ) is the second factor of f(x).

Hence, the two factors of the given polynomial f(x)

are ( x - 3 -√5) and ( x +6 ) .