One root of the following given equation $2{x^5} - 14{x^4} + 31{x^3} - 64{x^2} + 19x + 130 = 0$ is
$1$
$3$
$5$
$7$
If $x,\;y,\;z$ are real and distinct, then $u = {x^2} + 4{y^2} + 9{z^2} - 6yz - 3zx - zxy$ is always
If $\alpha, \beta $ and $\gamma$ are the roots of equation ${x^3} - 3{x^2} + x + 5 = 0$ then $y = \sum {\alpha ^2} + \alpha \beta \gamma $ satisfies the equation
The number of solutions of $\frac{{\log 5 + \log ({x^2} + 1)}}{{\log (x - 2)}} = 2$ is
The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0,$ is
The equation $\sqrt {3 {x^2} + x + 5} = x - 3$ , where $x$ is real, has