Let $S=\left\{\sin ^2 2 \theta:\left(\sin ^4 \theta+\cos ^4 \theta\right) x^2+(\sin 2 \theta) x+\right.$ $\left(\sin ^6 \theta+\cos ^6 \theta\right)=0$ has real roots $\}$. If $\alpha$ and $\beta$ be the smallest and largest elements of the set $S$, respectively, then $3\left((\alpha-2)^2+(\beta-1)^2\right)$ equals....................
$4$
$2$
$7$
$9$
The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is
The number of the real roots of the equation $(x+1)^{2}+|x-5|=\frac{27}{4}$ is ....... .
The number of real solution of equation $(\frac{3}{2})^x = -x^2 + 5x-10$ :-
Suppose $a$ is a positive real number such that $a^5-a^3+a=2$. Then,
The roots of $|x - 2{|^2} + |x - 2| - 6 = 0$are