For what values of a does the equation
2a−4x=4−a^2x
have a solution in the interval (−8, −2)?

The value of a which equation have 2 , -  

Step-by-step explanation:

Given expression as :

2 a - 4 x = 4 - a² × x

The equation lies in the interval ( - 8 , - 2 )

∵ equation lies in the interval , so it must satisfy the equation

So , 2 a - 4 × ( - 8 ) = 4 - a² × ( - 8 )

Or,  2 a + 32  = 4  + 8 a²

Or,    a + 16 = 2 + 4 a²

So, equation can be written as :

   4 a² - a - 14 = 0

Or, 4 a² - 8 a + 7 a - 14 = 0

Or, 4 a ( a - 2 ) + 7 ( a - 2 ) = 0

Or,      ( a - 2 ) ( 4 a + 7 ) = 0

∴    a = 2    And -  

Hence The value of a which equation have 2 , -  Answer

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