Question

Consider the polynomial $P ( x )=\left( x -\cos 36^{\circ}\right)\left( x -\cos 84^{\circ}\right)\left( x -\cos 156^{\circ}\right)$
The coefficient of $x^2$ is

• A. 0
• B. 1
• C. $-\frac{1}{2}$
• D. $\frac{\sqrt{5}-1}{2}$

Answer 1

Answer: (A)

$-\left(\cos 36^{\circ}+\cos 84^{\circ}+\cos 156^{\circ}\right) $
$\cos \left(60^{\circ}-24^{\circ}\right)+\cos \left(60^{\circ}+24^{\circ}\right)-\cos 24^{\circ} $
$=2 \cos 60^{\circ} \cos 24^{\circ}-\cos 24^{\circ} $
$=\cos 24^{\circ}-\cos 24^{\circ}=0 $