Mathematics - Quadratic Equation Question with Solution | TestHub

by newton's theorem $\begin{array}{rl}& {\mathrm{a}}_{\mathrm{n}+2}-\left({\mathrm{t}}^2-5\mathrm{t}+6\right){\mathrm{a}}_{\mathrm{n}+1}+{\mathrm{a}}_{\mathrm{n}}=0\\ & \therefore {\mathrm{a}}_{2025}+{\mathrm{a}}_{2023}=\left({\mathrm{t}}^2-5\mathrm{t}+6\right){\mathrm{a}}_{2024}\\ & \therefore \frac{{\mathrm{a}}_{2025}+{\mathrm{a}}_{2023}}{{\mathrm{a}}_{2024}}={\mathrm{t}}^2-5\mathrm{t}+6\\ & \because {\mathrm{t}}^2-5\mathrm{t}+6={\left(\mathrm{t}-\frac{5}{2}\right)}^2-\frac{1}{4}\\ & \therefore \text{ minimum value }=-\frac{1}{4}\end{array}$