Math Help - determine values of ω, that satisfy the roots given.....

i have an assignment question hopefully someone can help me with or point me in the right direction....

the question comes in 3 parts.i have done parts (i),(ii) i need to work out the 3rd part(iii).

(ii) if the roots of a cubic equation are x= -5/2 , x= 1/4, x= 3
determine the cubic expression by expansion, with these roots.


(iii) if x = Cos(2ω) in part (ii) of this question where ω is measured in radians. determine the values of ω, that satisfy the roots given that
0 ≤ ω ≥ 2(pi)


any help much appreciated

*

Hello, decoy808!

The question comes in 3 parts. I have done parts (i), (ii).

(ii) If the roots of a cubic equation are:
determine the cubic expression, by expansion, with these roots.

We have: .

Multiply [1]. [2] and [3]: .


Therefore: .

(iii) in part (ii) of this question, where is measured in radians.
Determine the values of that satisfy the roots, given that

We have: .


And we have three equations to solve:

. .

. .


. .

. . . .

thanks soroban it is a great help. i am still trying to understand a few things please excuse my ignorance

why did u subsitute (omega)for (theta)?

Hello, decoy808!

why did u subsitute (theta)for (omega)?

I's just easier to type.

My fingers are used to typing \-t-h-e-t-a,
. . while I have spell \-o-m-e-g-a very carefully.