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The numbers x (x²+ 1), - 1/2 x² and 6 are three consecutive terms of an AP. if x be real, then the next two terms of the AP are A) 14,22 B) 0,-8 C) -2,-10 D) noneof these Please solve fully with step

 The numbers x (x²+ 1), - 1/2 x² and 6 are three consecutive terms of an AP.  if x be real, then the next two terms of the AP are
A) 14,22
B) 0,-8
C) -2,-10
D) noneof these
Please solve fully with step

Grade:11

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
- x^2  = x^3 + x + 6
 
x^3 + x^2 + x+ 6 = 0
 
it is always increasing function hence only one real root is possible.
 
x = – 2 is only solution.
 
hence terms are
 
- 10  , – 2 , 6
common difference is 8.
 
hence next two terms are 14 and 22

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