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)

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