Question

A non zero value for c such that the solution set for the inequality x²+ 2cx- 6≤0 in the open interval (-3c, c) is :

Answer 1

Given  :  inequality x²+ 2cx- 6≤0 in the open interval (-3c, c)  

To find :  Value of c

Solution:

x²+ 2cx -  6 ≤ 0

=> (x + c)² - c² - 6 ≤ 0

=> (x + c)²  ≤ (c² + 6)

x  = - 3c

=> ( -3c + c)²  ≤ (c² + 6)

=> 4c²  ≤ (c² + 6)

=> 3c² ≤ 6

=> c² ≤ 2

x = c

=> ( c + c)²  ≤ (c² + 6)

=> 4c²  ≤ (c² + 6)

=> 3c² ≤ 6

=> c² ≤ 2

c lies  in [-√2 , √2]

integral value  1  &  - 1  both satisfies

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