The number of real roots of the equation $x^5+3 x^3+4 x+30=0$ is
The number of real roots of the equation $x^5+3 x^3+4 x+30=0$ is
$1$
$2$
$3$
$5$
Solution
Let $f(x)=x^5+3 x^3+4 x+30$
$\Rightarrow f^{\prime}(x)=5 x^4+9 x^2+4$
As $f^{\prime}(x)$ consist of the terms which has even powers of $x$. $f^{\prime}(x)>0$ for all $x \in \mathrm{R}$
Hence, the $f(x)=0$ has only one real root.