One factor of f(x)=4x^3-4x^2-16x+16 is (x – 2). what are all the roots of the function? use the remainder theorem.

The roots of f(x) are x=2, 1, -2

Step-by-step explanation:

Given polynomial is

One factor of above polynomial is (x – 2). we have to find all the roots of above polynomial. By applying synthetic division we find the quotient of above polynomial when divided by (x-2).

We get the coefficient

Hence, by remainder theorem,

                                               =

                                               =

                                               =

                                               =

To find roots, f(x)=0

⇒

⇒ x=2, 1, -2

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step-by-step explanation:

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x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)