The number of real roots of the equation `x^(2)+x+3+2 sin x=0, x in [- – InterviewSolution

1.	The number of real roots of the equation `x^(2)+x+3+2 sin x=0, x in [-pi,pi]`, isA. 2B. 3C. 4D. None of these
Answer» 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.

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