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 :
$5 \mathrm{S}_{6}+6 \mathrm{S}_{5}=2 \mathrm{S}_{4}$
$5 \mathrm{S}_{6}+6 \mathrm{S}_{5}+2 \mathrm{S}_{4}=0$
$6 \mathrm{S}_{6}+5 \mathrm{S}_{5}+2 \mathrm{S}_{4}=0$
$6 \mathrm{S}_{6}+5 \mathrm{S}_{5}=2 \mathrm{S}_{4}$
The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is
The sum of all integral values of $\mathrm{k}(\mathrm{k} \neq 0$ ) for which the equation $\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}$ in $x$ has no real roots, is ..... .
If $a \in R$ and the equation $ - 3{\left( {x - \left[ x \right]} \right)^2} + 2\left( {x - \left[ x \right]} \right) + {a^2} = 0$ (where $[x]$ denotes the greatest integer $\leq\,x$)has no integral solution ,then all possible values of $a$ lie in the interval
If $x$ is real, the function $\frac{{(x - a)(x - b)}}{{(x - c)}}$ will assume all real values, provided
The number of non-negative integer solutions of the equations $6 x+4 y+z=200$ and $x+y+z=100$ is