If $3$ distinct real number $a$,$b$,$c$ satisfy $a^2(a + p) = b^2 (b + p) = c^2 (c + p)$ where $p \in R$, then value of $bc + ca + ab$ is
$-p$
$p$
$0$
$\frac{{{p^2}}}{2}$
If $\sqrt {3{x^2} - 7x - 30} + \sqrt {2{x^2} - 7x - 5} = x + 5$,then $x$ is equal to
Product of real roots of the equation ${t^2}{x^2} + |x| + \,9 = 0$
The number of real solutions of the equation $e ^{4 x }+4 e ^{3 x }-58 e ^{2 x }+4 e ^{ x }+1=0$ is..........
The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0,$ is
The real roots of the equation ${x^2} + 5|x| + \,\,4 = 0$ are