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No of solutinos of the equation ( in image) in [0,2 π ] ?

No of solutinos of the equation ( in  image) in [0,2π] ?

Question Image
Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

x^{3} + 2x^{2} + 5x + 2cosx = 0
-2cosx = x^{3} + 2x^{2} + 5x
-2cosx = x(x^{2} + 2x + 5)
(x^{2} + 2x + 5)
does not have any real root, So the only real root of the equation
f(x) = x^{3} + 2x^{2} + 5x
is x = 0.
So the graph of f(x) is something similar to x2. On the other hand graph of -2cosx will not intersect with f(x). So there is no solution of the given function in image.

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