The product of the coefficients of quotient, when $f\left(x\right)=x^4-3x^2+x-1$ is divided by $(2x-1)$ is

$f\left(x\right)=x^4-3x^2+x-1$ is divided by $2x-1$

$\frac{1}{2}\frac{f\left(x\right)}{x-\frac{1}{2}}=\frac{1}{2}(x^3+\frac{1}{2}{x}^2-\frac{11}{4}x-\frac{3}{16})$

Quotient $=\frac{1}{2}{x}^3+\frac{1}{4}{x}^2-\frac{11}{8}x-\frac{3}{16}$

$\frac{1}{2}\times \frac{1}{4}\times \frac{(-)11}{8}\times \frac{(-)3}{16}$ $=\frac{33}{1024}$

Product of co-efficient = $\frac{33}{1024}$