If (x - 2)(x - p) = x² - ax + 6, then the value of (a - p) is?

Solution (By Examveda Team)

$$\eqalign{ & \left( {x - 2} \right)\left( {x - p} \right) = {x^2} - ax + 6 \cr & {x^2} - \left( {2 + p} \right)x + 2p = {x^2} - ax + 6 \cr & {\text{Comparision the cofficients}} \cr & 2 + p = a \cr & 2p = 6 \cr & \Leftrightarrow p = 3 \cr & 2 + 3 = a \cr & \Leftrightarrow a = 5 \cr & {\text{Then , }} \cr & p = 3,{\text{ }}a = 5 \cr & a - p = 5 - 3 \cr & \Leftrightarrow a - p = 2 \cr} $$