Question

If the number of real solutions of the equation x³ + 2x² + 5x + 2cos x = 0 in [0, 2π] is m, then the value of (m + 3) is...

Answer 1

The given equation is

⇒ x³ + 2x² + 5x + 2cosx = 0

⇒ x³ + 2x² + 5x = –2cosx

⇒ x(x² + 2x + 5) = – 2cosx

Clearly, it has no solution.

Thus m = 0

Hence, the value of (m + 3) is 3.