The number of non-negative integer solutions of the equations $6 x+4 y+z=200$ and $x+y+z=100$ is

If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$, then the other roots are

Let $a, b, c$ be the length of three sides of a triangle satisfying the condition $\left(a^2+b^2\right) x^2-2 b(a+c)$. $x+\left(b^2+c^2\right)=0$. If the set of all possible values of $x$ is the interval $(\alpha, \beta)$, then $12\left(\alpha^2+\beta^2\right)$ is equal to............................

If two roots of the equation ${x^3} - 3x + 2 = 0$ are same, then the roots will be

If $\sqrt {3{x^2} - 7x - 30} + \sqrt {2{x^2} - 7x - 5} = x + 5$,then $x$ is equal to

If ${x^2} + 2ax + 10 - 3a > 0$ for all $x \in R$, then