Question

For what values of a does the equation

2a−4x=4−a^2x
have a solution in the interval (−8, −2)?

Answer 1

The value of a which equation have 2 , -
`(7)/(4)`

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 -
`(7)/(4)`

Hence The value of a which equation have 2 , -
`(7)/(4)` Answer