Sequence-And-Series Question 667
Question: The roots of the equation $ {{(x-1)}^{2}}-4| x-1 |+3=0 $
Options:
A) Form an A.P.
B) Form a G.P.
C) Form an H.P.
D) Do not form any progression
Show Answer
Answer:
Correct Answer: A
Solution:
[a] The given eq. can be written as $ |x-1{{|}^{2}}-4|x-1|+3=0 $
$ \Rightarrow ,(|x-1|-3)(|x-1|-1)=0 $ If $ |x-1|-3=0\Rightarrow x-1=\pm 3\Rightarrow x=-2 $ or 4 If $ |x-1|-1=0\Rightarrow x-1=\pm 1\Rightarrow x=0 $ or 2 The four roots are -2, 0, 2, 4 and are in A.P.
BETA
