2007/ 001) Slightly hard cubic eqution

Find constants a, b, c, and d such that:

4x³ - 3x + √3/2=a * (x-b) * (x-c) * (x-d)

Solution
let p(x) be given polynomial

we reallize that sqrt(3)/2 = cos pi/6

so 4x^3-3x + cos pi/ 6= 0

or - cos pi/6 =-3x + 4x^3 = cos(3t) if x= cos t

so cos 3t = - cos pi/6 = cos 5pi/6

so 3t = 5pi/6 or 2pi-5pi/6 = 7pi/6 or 4pi-7pi/6 = 17pi/6
so t = 5pi/18 or 7pi/18 or 17pi/18

so b = cos 5pi/18,
c = cos 7pi/18
d= cos 17pi/18

as these are zeroes of polynomials

further comparing coefficient of x^3 we get a = 4