Find the no. of solutions of the equation x^(3)+2x^(2)+5x+2cosx=0,in the interval [0,2pi]
Find the no. of solutions of the equation x^(3)+2x^(2)+5x+2cosx=0,in the interval [0,2pi]
Diksha Bagade , 7 Years ago
Grade 12
Trigonometry> Find the no. of solutions of the equation...
1 Answers
Arun
Last Activity: 7 Years ago
Let f(x) = x3 + 2x2 + 5x +2 cosx
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] .
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