$\large\frac{dy}{dx}$$=1$ passes through $\large[$$0,\large\frac{3}{2}]$ and $\large\frac{dy}{dx}$$=2$ passes through $[0,1]$ represents two curve which passes through a point whose coordinates are zeroes of a quadratic polynomial . The quadratic equation is gradient polynomial. Find sum of coefficients of $x^3,x^2,x$

Question

$(a)\;\frac{3}{4}\\(b)\;\frac{1}{4}\\ (c)\;\frac{2}{3} \\ (d)\;\frac{1}{3}$