If (px³ - 8x² - qx + 1), the expression is completely divisible by the expression (3x² - 4x + 1). Then what will be the value of p and q respectively?

Solution (By Examveda Team)

$$\eqalign{ & 3{x^2} - 4x + 1 = 0 \cr & 3{x^2} - 3x - x + 1 = 0 \cr & \left( {3x - 1} \right)\left( {x - 1} \right) = 0 \cr & 3x - 1 = 0,\,\,x - 1 = 0 \cr & \Rightarrow x = 1,\,\frac{1}{3} \cr & {\text{Put }}x = 1{\text{ in }}p{x^3} - 8{x^2} - qx + 1 \cr & \Rightarrow p - 8 - q + 1 = 0 \cr & \Rightarrow p - q = 7 \cr & {\text{Go through the option C}} \cr & p = \frac{{33}}{4},\,q = \frac{5}{4} \cr & \Rightarrow \frac{{33 - 5}}{4} = 7 \cr & \Rightarrow 7 = 7 \cr} $$