Let $a, b, c$ be non-zero real numbers such that $a+b+c=0$, let $q=a^2+b^2+c^2$ and $r=a^4+b^4+c^4$. Then,
$q^2 < 2 r$ always
$q^2=2 r$ always
$q^2 > 2 r$ always
$q^2-2 r$ can take both positive and negative values
Product of real roots of the equation ${t^2}{x^2} + |x| + \,9 = 0$
The number of integers $n$ for which $3 x^3-25 x+n=0$ has three real roots is
Number of positive integral values of $'K'$ for which the equation $k = \left| {x + \left| {2x - 1} \right|} \right| - \left| {x - \left| {2x - 1} \right|} \right|$ has exactly three real solutions, is
The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is :
The number of solutions of the equation $\log _{(x+1)}\left(2 x^{2}+7 x+5\right)+\log _{(2 x+5)}(x+1)^{2}-4=0, x\,>\,0$, is $....$