Question

If cos pi/7, cos 3pi/7, cos 5pi/7 are the roots of the equation ax^3+bx^2+cx+d=0, then

Answer 1

$sum \: of \: the \: roots = - coeff \:o of {x}^{2} \div coeff \: of \: {x}^{3} = - b \div a \\ \cos(\pi \div 7) + \cos(3\pi \div 7) + \cos(5\pi \div 7) = - b \div a$

prpdu

$product \: of \: roots = - d \div a = \cos(\pi \div 7) \cos(3\pi \div 7) \cos(5\pi \div 7) = - d \div a$