Question

The minimum integral value of $a$ for which $\frac{x^2-x}{1-ax}$ attains all real values, is

Answer 1

The roots of numerator are $0,1$ and the roots of denominator is $\frac{1}{a}.$
Now, to attain all values roots denominator must be lies between the roots of numerator.
$\therefore 0<\frac{1}{a}<1\Rightarrow 0<\frac{1}{a};\frac{1}{a}<1\Rightarrow a>0;a>1\therefore a>1$

Hence, the minimum integral value of $a$ is $2$.