### Theory of Equations

goals
Find the equation whose root are square of the root are ${x^3} - 2{x^2} - x + 5 = 0$

$|x - 3| + 2|x + 1| = 4$. Find $x$?
If $x - 2$ and $x - \dfrac{1}{2}$ both are the factors of the polynomial $nx^2 - 5x + m$, then show that $m = n = 2$.
The least integral value of $x$ for which $33 - x(2 + 3x) > 0$ is
Simplify $\sqrt { 1+{ \left( \cfrac { { x }^{ 4 } }{ -2{ x }^{ 2 } } \right) }^{ 2 } }$