• # question_answer The number of solution of the equation ${{x}^{3}}+{{x}^{2}}+4x+2\,\sin \,x=0$ is A)  2                                 B)  3                 C)  1                                 D)  8

$f(x)={{x}^{3}}+{{x}^{2}}+4x+2\,\,\sin \,\,x=0$ $f'(x)=3{{x}^{2}}+2x+4+2\,\,\cos \,\,x$ For $\cos \,\,x=\pm \,1$ $f'(x)=3{{x}^{2}}+2x+4\pm 2$ $\Rightarrow$            $(\because \,\,D={{b}^{2}}-4ac)$ Hence, only one solution exist, i.e., $x=0$.