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Maths-

General

Easy

Question

The number of solutions the equation $x to the power of 3 end exponent plus 2 x to the power of 2 end exponent plus 5 x plus 2 c o s invisible function application x equals 0 text in end text left square bracket 02 pi right square bracket$ is

0
1
2
3

The correct answer is: 0

$text Hint: For the increasing function end text f to the power of ´ end exponent left parenthesis x right parenthesis greater than 0 text . end text$
Let
$f left parenthesis x right parenthesis equals x to the power of 3 end exponent plus 2 x to the power of 2 end exponent plus 5 x equals x open parentheses x to the power of 2 end exponent plus 2 x plus 5 close parentheses$
The term in the bracket has no root
Also, f’(x) > 0 and so f(x) is always increasing.
From the graph (Fig. 3.10), it is clear that in (0, 2p) equations do not have any solution.

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