If $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{ax}}^3+{\mathrm{bx}}^2+\mathrm{cx}+\mathrm{d}$, (a, b, c, d are rational nos.) and roots of $\mathrm{f}\left(\mathrm{x}\right)=0$ are eccentricities of a parabola and a rectangular hyperbola then a + b + c + d equals

Eccentricities of parabola and rectangular hyperbola are 1,$\sqrt{2}$

Roots are $1, \sqrt{2}, -\sqrt{2}$

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)=(x-1)(x-\sqrt{2})(x+\sqrt{2}) \\ ={\mathrm{x}}^3-{\mathrm{x}}^2-2\mathrm{x}+2=0 \\ By comparision a=1,b=-1,c=-2,d=2 \\ Now \mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}=0 \end{gathered}$$