Question

What will be the polynomial of lowest degree whose root is?

Answer 1

Find the least degree Polynomial with Integer Coefficients whose one of the roots is cos(12∘)

My Try: we know that

cos(5x)=cos5x−10cos3xsin2x+5cosxsin4x

Putting x=12∘ and Converting sin to cos we have

12=x5−10x3(1−x2)+5x(1−2x2+x4)

⟹

32x5−40x3+10x−1=0