One root of f(x)=x3-9x2+26x-24 is x=2. what are all the roots of the function? use the remainder theorem.

All roots of the given function are, 2 , 3 and 4

Step-by-step explanation:

Given the function f(x) =

Also, it given that x=2 is a root of the function f(x).

So,  (x-2) is a factor of f(x).

Remainder theorem states that if a function is divided by (x-a), then the remainder is equal to f(a). If a function f(a) is equal to 0, therefore a is the root of the function.

We use synthetic method to divide f(x) by (x-2) as also shown in figure below;

To find the roots of the function f(x) equate f(x) = 0.

we have;

By zero product property states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0.

x = 2 , 3 and 4.

Therefore, the roots of the given functions are; 2 , 3 and 4.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .