# Solve over the interval [0,2π) 2(cos^2)x+cosx=0

Question
Functions
Solve over the interval PSK[0,2π) 2(cos^2)x+cosx=0ZSK

2021-02-06
The terms of $$\displaystyle{2}{\left({\cos}^{{2}}\right)}{x}+{\cos{{x}}}={0}$$ have a common factor of $$\displaystyle{\cos{{x}}}$$. Factoring out $$\displaystyle{\cos{{x}}}{t}{h}{e}{n}{g}{i}{v}{e}{s}{P}{S}{K}{\cos{{x}}}{\left({2}{\cos{{x}}}+{1}\right)}={0}$$.
The Zero Product Property states that if ab=0, then a=0 or b=0. Therefore, if cosx(2cosx+1)=0ZSK, then $$\displaystyle{\cos{{x}}}={0}$$ \ or \ $$\displaystyle{2}{\cos{{x}}}+{1}={0}$$.
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