Complex Numbers And Quadratic Equations question 193
Question: If $ x^{2}+px+q=0 $ is the quadratic equation whose roots are a - 2 and b - 2 where a and b are the roots of $ x^{2}-3x+1=0 $ , then [Kerala (Engg.) 2002]
Options:
A) $ p=1,q=5 $
B) $ p=1,q=-5 $
C) $ p=-1,q=1 $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
$ a+b=3 $ , $ ab=1 $ and $ -p=a-2+b-2 $ , $ q=(a-2)(b-2) $
Þ $ -p=a+b-4 $ , $ q=ab-2(a+b)+4 $
$ \Rightarrow -p=3-4 $ and $ q=1-2(3)+4 $
Þ $ (p,q)=(1,-1) $ .
BETA
