If  $f\left(x\right)=a{x}^3+b{x}^2+cx+d$, ( $a,b,c,d$ are rational numbers) and the roots of $f\left(x\right)=0$ are eccentricities of a parabola and a rectangular hyperbola then $a+b+c+d$ equal to

We know that eccentricity of a parabola and rectangular hyperbola are $1,\sqrt{2}$ . Also irrational roots occur in conjugate pair
Roots of $f\left(x\right)=0$ are  $1,\sqrt{2},-\sqrt{2}$

$f\left(x\right)=(x-1)(x-\sqrt{2})(x+\sqrt{2})=x^3-x^2-2x+2$

$a+b+c+d=1-1-2+2=0$