Find coefficient of x^2 and x

Question

anonymous · Answer

Consider the polynomial P(x)= (x-cos 36)(x-cos 84)(x-cos 156)

loser66 · Answer

it's not hard, just tedious, you can do it by yourself :)

anonymous · Answer

so there must be an easy way

ganeshie8 · Answer

use Vieta's formulas

anonymous · Answer

I don't know them ,

ganeshie8 · Answer

x^3 + bx^2 + cx + d

sum of roots = -b
sum of products of two roots = c
product of roots  = d

anonymous · Answer

is that called vieta i didn't knew sry

ganeshie8 · Answer

yes but u don't need to know it, just expand the cubic and see what u get for coefficients

anonymous · Answer

yeah wait

ganeshie8 · Answer

$$\large    P(x)= (x-\cos 36)(x-\cos 84)(x-\cos 156)$$

using vieta's formula,
coefficient of x^2 would be $-(\cos 36 + \cos 84 + \cos 156)$

simplify if possible

anonymous · Answer

yes getting the same

ganeshie8 · Answer

and that magically turns out to be 0

anonymous · Answer

attachment

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=%5Ccos+36+%2B+%5Ccos+84+%2B+%5Ccos+156

ganeshie8 · Answer

how did u get 0 ?

anonymous · Answer

I had a sum where i got this as i result and it was 0

anonymous · Answer

had done

anonymous · Answer

I can evaluate it though , i am not sure about cos 24 and cos96

ganeshie8 · Answer

ok the x coefficient would be :

$$\cos 36 \cos 84  + \cos 84 \cos 156+ \cos 156\cos 36$$

ganeshie8 · Answer

i need to think a bit on how to simplify these

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=%5Ccos+36+%5Ccos+84++%2B+%5Ccos+84+%5Ccos+156%2B+%5Ccos+156%5Ccos+36

ganeshie8 · Answer

it evaluates to -3/4 somehow

anonymous · Answer

answer is -3/2