Sequence And Series Question 99
Question: If the roots of the equation $ x^{3}-12x^{2}+39x-28=0 $ are in A.P., then their common difference will be
[UPSEAT 1994, 99, 2001; RPET 2001]
Options:
A) $ \pm 1 $
B) $ \pm 2 $
C) $ \pm 3 $
D) $ \pm 4 $
Show Answer
Answer:
Correct Answer: C
Solution:
Let a - d, a, a + d be the roots of the equation $ x^{3}-12x^{2}+39x-28=0 $ Then $ (a-d)+a+(a+d)=12 $ and $ (a-d),a,(a+d)=28 $
Þ $ 3a=12 $ and $ a,(a^{2}-d^{2})=28 $
Þ $ a=4 $ and $ a,(a^{2}-d^{2})=28 $
Þ $ 16-d^{2}=7\Rightarrow d=\pm ,3 $ .
BETA
