If $x$ is real, then the value of ${x^2} - 6x + 13$ will not be less than

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

Let $f: R \rightarrow R$ be the function $f(x)=\left(x-a_1\right)\left(x-a_2\right)$ $+\left(x-a_2\right)\left(x-a_3\right)+\left(x-a_3\right)\left(x-a_1\right)$ with $a_1, a_2, a_3 \in R$.Then, $f(x) \geq 0$ if and only if

The product of the roots of the equation $9 x^{2}-18|x|+5=0,$ is

If $\alpha , \beta $ are the roots of the equation $x^2 - 2x + 4 = 0$ , then the value of $\alpha ^n +\beta ^n$ is

The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is