Will you find the value of roots?

Geometry Level 5

If the cubic polynomial whose roots are cos(2π7),cos(4π7) \cos \left( \dfrac{2\pi}7 \right),\cos \left( \dfrac{4\pi}7 \right) and cos(6π7) \cos \left( \dfrac{6\pi}7 \right) is of the form abx3+acx2adx1  , a^b x^3 + a^c x^2 - a^d x - 1 \; , where a,b,ca,b,c and dd are primes, find a+b+c+da+b+c+d.

Hint:

z2n+11=(z1)k=1n(z22cos2πk2n+1z+1){z^{2n+1}-1 =(z-1) \cdot \prod_{k=1}^{n}\left(z^{2}-2 \cdot \cos \dfrac{2\pi k}{2n+1}z +1 \right) }

×

Problem Loading...

Note Loading...

Set Loading...