Question

Consider the polynomial P(x)= (x-cos36)(x-cos84)(x-cos156) find coefficients of x^2 and x

Answer 1

let cos36 = a
cos84 =b
cos156 =c

hence,
p (x) =(x - a )(x - b)( x - c )
=x^3-(a+b+c)x^2+(ab+bc+ca) x-abc

coefficient of x^2 = -(a+b+c)
e.g
-(a +b+c)= - (cos36 +cos84+cos156)

also coefficient of x =(ab+bc+ca)
=(cos36.cos84+cos84.cos156+cos156.cos36)