Q53 / 160 · AP EAMCET 2016 · Mathematics

The number of real roots of the equation $x^5+3 x^3+4 x+30=0$ is

Correct answer
A
$1$
B
$2$
C
$3$
D
$5$

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.

Hence, the correct answer is option: 'A'.

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