$(1)$ If $k\in\mathbb{R}$. Then minimum no. of distinct possible real roots of the equation
$(3x^2+kx+3)(x^2+kx-1) = 0.$
$\bf{My\; Try::}$ Discriminant of quadratic equation $3x^2+kx+3 = 0$ is $D_{1} = (k^2-36)$
$\bullet $ If $|k|<6\:,$ Then $D_{1}<0\;\;,\bullet\; $ If $|k|=6,$ Then $D_{1}=0\;,$ If $|k|>6\;,$ Then $D_{1}>0$
And Discriminant of quadratic equation $x^2+kx-1 = 0$ is $D_{2} = (k^2+4)>0\;\forall \;k\;\in \mathbb{R}$
So we can conclude that $(3x^2+kx+3)(x^2+kx-1)=0$ has Max.$2$ distinct real roots, If $|k|>6$
and $2$ equal roots, If $|k|=6.$
and no real roots , If $|k|<6.$
So Min. possible distinct real roots of the equation $(3x^2+kx+3)(x^2+kx-1)=0$ is $=0$
But answer given as $ = 2$
plz help me, Thanks