Question

The number of solutions of the equation x² + 2x² + 5x + 2 cos x in [0,2π] is

(A)  0

(B)  1

(C)  2

(D)  3

Answer 1

Correct option  (A) 0

x² + 2x² + 5x + 2 cos x = 0

⇒ x² + 2x² + 5x = - 2 cos x

Now,

y = x(x² + 2x + 5) = -2cosx

⇒ y = x(x² + 2x + 5)

If x ∈[0,2π], then number of solutions is zero.