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?
A. $$\left( {\frac{{21}}{4},\,\frac{{15}}{8}} \right)$$
B. $$\left( {6,\,1} \right)$$
C. $$\left( {\frac{{33}}{4},\,\frac{5}{4}} \right)$$
D. $$\left( {1,\,6} \right)$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & 3{x^2} - 4x + 1 = 0 \cr & 3{x^2} - 3x - x + 1 = 0 \cr & \left( {3x - 1} \right)\left( {x - 1} \right) = 0 \cr & 3x - 1 = 0,\,\,x - 1 = 0 \cr & \Rightarrow x = 1,\,\frac{1}{3} \cr & {\text{Put }}x = 1{\text{ in }}p{x^3} - 8{x^2} - qx + 1 \cr & \Rightarrow p - 8 - q + 1 = 0 \cr & \Rightarrow p - q = 7 \cr & {\text{Go through the option C}} \cr & p = \frac{{33}}{4},\,q = \frac{5}{4} \cr & \Rightarrow \frac{{33 - 5}}{4} = 7 \cr & \Rightarrow 7 = 7 \cr} $$Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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