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. 3
C. 4
D. None of these

Answer 1

Correct Answer - D
We have,
`x^(2)+x+3+2 sin x=0`
`implies x^(2)+x+3=-2 sin implies(x+(1)/(2))^(2)+(11)/(4)=-2 sin x`
We observe that `LHS gt (11)/(4) gt 2` for all x whereas RHS lies between -2 and 2 Hence, the given equation has no solution.