The solutions of the quadratic equation ${(3|x| - 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x - 3)} $ are given by
$ \pm 1/9,\; \pm 2$
$ - 1/9,\;2$
$1/9,\; - 2$
$ - 1/9,\; - 2$
For what value of $\lambda$ the sum of the squares of the roots of ${x^2} + (2 + \lambda )\,x - \frac{1}{2}(1 + \lambda ) = 0$ is minimum
If ${x^2} + px + 1$ is a factor of the expression $a{x^3} + bx + c$, then
The number of integers $n$ for which $3 x^3-25 x+n=0$ has three real roots is
If $\alpha, \beta $ and $\gamma$ are the roots of the equation $2{x^3} - 3{x^2} + 6x + 1 = 0$, then ${\alpha ^2} + {\beta ^2} + {\gamma ^2}$ is equal to
If the inequality $kx^2 -2x + k \geq 0$ holds good for atleast one real $'x'$ , then the complete set of values of $'k'$ is