Find the no. of solutions of the equation x^(3)+2x^(2)+5x+2cosx=0,in the interval [0,2pi]

Þ f¢(x)  = 3x2 +4x  + 5 – 2 sinx

= 3  

Now   "x  ( as  -1 £ sinx £ 1)

Þ f¢(x) > 0 " x

Þ f(x) is  an increasing  function.

Now  f(0) = 2

Þ f(x) = 0  has  no solution in [ 0, 2p] .