Given $\left|{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}\right|\le \left|{\mathrm{Ax}}^2+\mathrm{Bx}+\mathrm{C}\right|,\mathrm{\forall }\mathrm{x}\in \mathrm{R},\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{A},\mathrm{B},\mathrm{C}\in \mathrm{R}$ and d = b²–4ac>0 and D=B²–4AC > 0. Then which of the following statements are true

Let $\mathrm{\alpha } \mathrm{\&} \mathrm{\beta }$ are the roots of Ax² + Bx + c = 0
$\Rightarrow \because \left|{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}\right|\le \left|{\mathrm{Ax}}^2+\mathrm{Bx}+\mathrm{c}\right|\mathrm{\forall }\in \mathrm{R}$
ax² + bx + c = 0 also has $\mathrm{\alpha }, \mathrm{\beta }$ as roots
$$\begin{gathered} \Rightarrow \left|{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}\right|=\left|\mathrm{a}\right||\mathrm{x}-\mathrm{\alpha }||\mathrm{x}-\mathrm{\beta }|=\left|\mathrm{A}\right||\mathrm{x}-\mathrm{\alpha }||\mathrm{x}-\mathrm{\beta }| \\ \begin{array}{r}\Rightarrow \left|\mathrm{a}\right|\le \left|\mathrm{A}\right|\mathrm{\&}(\mathrm{\alpha }-\mathrm{\beta }{)}^2=(\mathrm{\alpha }+\mathrm{\beta }{)}^2-4\mathrm{\alpha \beta }\\ \Rightarrow \frac{{\mathrm{b}}^2-4\mathrm{ac}}{{\mathrm{a}}^2}=\frac{{\mathrm{B}}^2-4\mathrm{AC}}{{\mathrm{A}}^2}\Rightarrow \left|\mathrm{d}\right|\le \left|\mathrm{D}\right|\end{array} \end{gathered}$$