Find the number of solutions of the equation `sinx=x^2+x+1.`

Explanation

Let f(x) = sin x and `g(x) = x^(2) + 2x + 1 = (x + 1)^(2)`
Graphs of y = sin x and `y = (x + 1)^(2)` are as shown in the following figure.

Since the curvey `y = (x + 1)^(2)` meets the y - axis at (0, 1), it never intersects y = sin x. Hence no solution.