If $\alpha_1, \alpha_2, \alpha_3 \ldots, \alpha_n$ are real numbers, $\alpha_1
eq 0$ and $z=\cos heta+i \sin heta$ is a root of the equation $\alpha_1+\alpha_2 z+\alpha_3 z^2+\ldots+\alpha_n z^{n-1}+z^n=0$, then $\alpha_1 \cos n heta+\alpha_2 \cos (n-1) heta+\ldots+\alpha_n \cos heta=$

Question

If $\alpha_1, \alpha_2, \alpha_3 \ldots, \alpha_n$ are real numbers, $\alpha_1 
eq 0$ and $z=\cos 	heta+i \sin 	heta$ is a root of the equation $\alpha_1+\alpha_2 z+\alpha_3 z^2+\ldots+\alpha_n z^{n-1}+z^n=0$, then $\alpha_1 \cos n 	heta+\alpha_2 \cos (n-1) 	heta+\ldots+\alpha_n \cos 	heta=$

Aicharya · Accepted Answer

No solution. Refer to answer key.

If $\alpha_1, \alpha_2, \alpha_3 \ldots, \alpha_n$ are real numbers, $\alpha_1 \neq 0$ and $z=\cos \theta+i…

Solution