Question

The number of real roots of the equation $x^2+x+3+2\sin x=0,x\in [-\pi ,\pi ]$ is

• A. $2$
• B. $4$
• C. $6$
• D. none of these

Answer 1

The correct option is D none of these

$x^2+x+3+2sin\left(x\right)=0$

$(x+\frac{1}{2}{)}^2-\frac{1}{4}+3+2sin(x)=0$

$(x+\frac{1}{2}{)}^2+2sin(x)+\frac{11}{4}=0\to (i)$

$sin\left(x\right)=[-1,1]$ and $-2\le 2sin\left(x\right)\le 2$

Its clear that equation $\left(i\right)$ can not be equal to in the interval

$xϵ[-\pi ,\pi ]$

Hence, option 'D' is correct.