For what values of a does the equation 2a−4x=4−a^2x have a solution in the interval (−8, −2)?
Accepted Solution
A:
Answer:The value of a which equation have 2 , - [tex]\frac{7}{4}[/tex] 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 = 0Or, 4 a² - 8 a + 7 a - 14 = 0Or, 4 a ( a - 2 ) + 7 ( a - 2 ) = 0Or, ( a - 2 ) ( 4 a + 7 ) = 0∴ a = 2 And - [tex]\frac{7}{4}[/tex] Hence The value of a which equation have 2 , - [tex]\frac{7}{4}[/tex] Answer