In the equation ${x^3} + 3Hx + G = 0$, if $G$ and $H$ are real and ${G^2} + 4{H^3} > 0,$ then the roots are
All real and equal
All real and distinct
One real and two imaginary
All real and two equal
Consider the following two statements
$I$. Any pair of consistent liner equations in two variables must have a unique solution.
$II$. There do not exist two consecutive integers, the sum of whose squares is $365$.Then,
If $x, y$ are real numbers such that $3^{(x / y)+1}-3^{(x / y)-1}=24$ then the value of $(x+y) /(x-y)$ is
The number of real solutions of the equation $|x{|^2}$-$3|x| + 2 = 0$ are
If graph of $y = ax^2 -bx + c$ is following, then sign of $a$, $b$, $c$ are
The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is