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

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

Step-by-step 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 ) .

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

10 you would take 50/ .2

step-by-step explanation: