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  4. The number of real roots of the equation x5+3 x3+4 x+30=0 is

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

AP EAMCETAP EAMCET 2016

Solution:

Let $f(x)=x^{5}+3 x^{3}+4 x+30$
$\Rightarrow f^{'}(x)=5 x^{4}+9 x^{2}+4$
$\Rightarrow f^{'}(x)>0$ for all $x \in R$
Hence, the $ f(x)=0$ has only one real root.