If $x ^ { 2 } + ( a - b ) x + ( 1 - a - b ) = 0$ where $a , b$ Î $R$ then find the values of $a$ for which equation has unequal real roots for all values of $b$.
Let $f ( x )$ be a differentiable function with $f ^ { \prime } ( 1 ) = 4$ and $f ^ { \prime } ( 2 ) = 6$, where $f ^ { \prime } ( c )$ is the derivative of $f ( x )$ at $x = c$. Then the limit of $\frac { f \left( 2 + 2 h + h ^ { 2 } \right) - f ( 2 ) } { f \left( 1 + h - h ^ { 2 } \right) - f ( 1 ) }$, as $h \rightarrow 0$,
If $x ^ { 2 } + ( a - b ) x + ( 1 - a - b ) = 0$ where $a , b$ Î $R$ then find the values of $a$ for which equation has unequal real roots for all values of $b$.