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
$3/2$
$1$
$1/2$
$11/4$
The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is :
The sum of the cubes of all the roots of the equation $x^{4}-3 x^{3}-2 x^{2}+3 x+1=10$ is
The number of non-negative integer solutions of the equations $6 x+4 y+z=200$ and $x+y+z=100$ is
Below are four equations in $x$. Assume that $0 < r < 4$. Which of the following equations has the largest solution for $x$ ?
The complete solution of the inequation ${x^2} - 4x < 12\,{\rm{ is}}$