Complex Numbers And Quadratic Equations question 10
Question: If $ x^{2}-3x+2 $ be a factor of $ x^{4}-px^{2}+q, $ then $ (p,q)= $ [IIT 1974; MP PET 1995; Pb. CET 2001]
Options:
A) (3, 4)
B) (4, 5)
C) (4, 3)
D) (5, 4)
Show Answer
Answer:
Correct Answer: D
Solution:
$ x^{2}-3x+2 $ be factor of $ x^{4}-px^{2}+q=0 $ Hence $ (x^{2}-3x+2)=0\Rightarrow (x-2)(x-1)=0 $
Þ $ x=2,1, $ putting these values in given equation so $ 4p-q-16=0 $ …..(i) and $ p-q-1=0 $ …..(ii) Solving (i) and (ii), we get (p, q)=(5, 4)
BETA
