Question

Find the number of solutions of the equation $\sin x=x^2+x+1$

Answer 1

We know, $-1\le \sin x\le 1$
$\therefore x^2+x+1=-1$ or $x^2+x+1=1$
$x^2+x+2=0$ or $x^2+x=0$
$x=\frac{-1\pm \sqrt{1-8}}{2}$ or $x(x+1)=0$
Imaginary solution $x=0,-1$