The no. of roots of equation x^2+x+3+2sinx=0,x belongs to (-180 to +180) is?

x^2+x+3+2sinx
= ( x^2+ x + 1/4)+ 11/4 + 2 sin x
= (x+ 1/2)^2 + 11/4 + 2 sin x

the lowest value of (x+ 1/2)^2 = 0
lowest value of 2 sin x = - 2

so lowest value = 11/4 -2 = 3/4

so it can never be zero

so ans is zero