No. of real roots of the equation $x^{3} + x^{2}$ + 10x + sin x = 0, is :

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Solution

The correct option is A

$f (x) =$ $x^{3} + x^{2} + 10 x + s i n x$

$\Rightarrow$ f '(x) = $3 x^{2}$ $+ 2 x + 10 + c o s x$

$= 3$ $(\frac{x + 1}{3})^{2} + \frac{29}{3}$ $+ c o s x > 0 \forall x$

$\Rightarrow$ f(x) has only on real root

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