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The number of real roots of the equation $x^5+3 x^3+4 x+30=0$ is
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Verified Answer
The correct answer is:
$1$
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.
$\Rightarrow f^{\prime}(x)=5 x^4+9 x^2+4$
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.
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