Finding the Nature of Roots

Let $f(x)=x^4+16x-12$ .
By using Descartes Rule of Sign and counting the number of sign changes in $f(x)$ we will get the total number of positive roots . $\implies f(x)=x^4+16x-12\implies (+ \boxed{+ -})$ .
$\therefore$ It will have maximum $1$ positve root .

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Now putting $-x$ in $f(x)$ and counting number of sign changes again , will give the total number of negative roots.

$f(-x)=(-x)^4+16(-x)-12$
$\implies f(-x)=x^4-16x-12$ $\implies (\boxed{+ -} -)$
$\therefore$ It will have maximum $1$ negative root .

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$\therefore$ It has $1$ positive and $1$ negative root.

$\therefore$ Total number of real roots = Total number of positive roots + Total number of negative roots = $1+1$ = $2$
$\therefore$ Total number of complex roots =Degree of polynomial - Total number of real roots = $4-2 = 2$ .