Question

determine an equation in simplified form, for a function with the zeroes of 2+ square root of 5 / 2- square root of 5 and 0., and with its graph passing through the point (2,20)

Answer 1

\[2-\sqrt{5}, 2+\sqrt{5}\]

Answer 2

?

Answer 3

you are looking for an equation with specific roots right?

Answer 4

yah

Answer 5

\[(x-(2-\sqrt{5}))(x-(2+\sqrt{5}))\]

Answer 6

there it is if you sub either of those numbers into it you will set the equation to zero

Answer 7

what are you not understanding?

Answer 8

and x too right ?

Answer 9

x(x−(2−5√))(x−(2+5√))

Answer 10

you can do this with any equation with specific roots
if you wanted an equation with roots of 5, and 3

(x-5)(x-3)

Answer 11

if one of the roots is zero then yes

Answer 12

if you had roots
-5, 2

(x-(-5)) (x-2)
=
(x+5)(x-2)

Answer 13

then I sub the point in to find a right?

Answer 14

no foil it out first

x^(3)-4x^(2)-x = y
then sub x= 2 into it and see how far it is away from 20
you get

-10
so take your original equation and mutliply the entire thing by something that makes it equal to 20, -2 will do that :)

-2(x^(3)-4x^(2)-x)

Answer 15

now you have your answer

Answer 16

do you get it? it really isn't hard at all

Answer 17

where did u get this : x^(3)-4x^(2)-x = y

Answer 18

1. Put roots into the form (x - (root))(x - (root))
2. Sub the x value of the point into the equation and see what you get as a y value
3. multiply the entire equation by something that will give you the y value you are looking for.

Well if you expended the equation you just generated for this question you would know

Answer 19

i think u right, sorry but still i don't understand it :(

Answer 20

I dont think I can explain it anymore than I already have, if you dont understand the concept take a break and come back and read it

Answer 21

how about this ? create a cubic polynomial inequality for which x=3 or x<=-2 is the solution.

Answer 22

you can have two solutions for that
(x - 3)(x - (-2))(x - 3) = (x -3)(x + 2)(x-3)
or
(x - 3)(x - (-2))(x - (-2)) = (x - 3)(x + 2)(x + 2)

if you expanded this you would end up with a cubic root equation with the roots specified