Consider the polynomial $f(x)=1+2 x+3 x^2+4 x^3$. Let $s$ be the sum of all distinct real roots of $f(x)$ and let $t=|s|$.
$1.$ The real number $s$ lies in the interval
$(A)$ $\left(-\frac{1}{4}, 0\right)$ $(B)$ $\left(-11,-\frac{3}{4}\right)$
$(C)$ $\left(-\frac{3}{4},-\frac{1}{2}\right)$ $(D)$ $\left(0, \frac{1}{4}\right)$
$2.$ The area bounded by the curve $y=f(x)$ and the lines $x=0, y=0$ and $x=t$, lies in the interval
$(A)$ $\left(\frac{3}{4}, 3\right)$ $(B)$ $\left(\frac{21}{64}, \frac{11}{16}\right)$
$(C)$ $(9,10)$ $(D)$ $\left(0, \frac{21}{64}\right)$
$3.$ The function $f^{\prime}(x)$ is
$(A)$ increasing in $\left(-t,-\frac{1}{4}\right)$ and decreasing in $\left(-\frac{1}{4}, t\right)$
$(B)$ decreasing in $\left(-t,-\frac{1}{4}\right)$ and increasing in $\left(-\frac{1}{4}, t\right)$
$(C)$ increasing in (-t, t) $(D)$ decreasing in ( $-\mathrm{t}, \mathrm{t})$
Give the answer question $1,2$ and $3.$