The roots of $|x - 2{|^2} + |x - 2| - 6 = 0$are

Let $a, b, c, d$ be real numbers such that $|a-b|=2$, $|b-c|=3,|c-d|=4$. Then, the sum of all possible values of $|a-d|$ is

Let, $\alpha, \beta$ be the distinct roots of the equation $\mathrm{x}^2-\left(\mathrm{t}^2-5 \mathrm{t}+6\right) \mathrm{x}+1=0, \mathrm{t} \in \mathrm{R}$ and $\mathrm{a}_{\mathrm{n}}=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}$. Then the minimum value of $\frac{\mathrm{a}_{2023}+\mathrm{a}_{2025}}{\mathrm{a}_{2024}}$ is

The two roots of an equation ${x^3} - 9{x^2} + 14x + 24 = 0$ are in the ratio $3 : 2$. The roots will be

Let $x, y, z$ be non-zero real numbers such that $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=7$ and $\frac{y}{x}+\frac{z}{y}+\frac{x}{z}=9$, then $\frac{x^3}{y^3}+\frac{y^3}{z^3}+\frac{z^3}{x^3}-3$ is equal to

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