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
$3/2$
$1$
$1/2$
$11/4$
Consider a three-digit number with the following properties:
$I$. If its digits in units place and tens place are interchanged, the number increases by $36$ ;
$II.$ If its digits in units place and hundreds place are interchanged, the number decreases by $198 .$
Now, suppose that the digits in tens place and hundreds place are interchanged. Then, the number
Let $\alpha$ and $\beta$ be the roots of the equation $5 x^{2}+6 x-2=0 .$ If $S_{n}=\alpha^{n}+\beta^{n}, n=1,2,3 \ldots$ then :
The equation $e^{4 x}+8 e^{3 x}+13 e^{2 x}-8 e^x+1=0, x \in R$ has:
The sum of integral values of $a$ such that the equation $||x\ -2|\ -|3\ -x||\ =\ 2\ -a$ has a solution
Product of real roots of the equation ${t^2}{x^2} + |x| + \,9 = 0$