Question

Find the value of a and b for which ax^3 -11x^2 +ab +b is exactly divisible by x^2- 4x -5

Answer 1

★ QUADRATIC RESOLUTION ★

Given equation :

ax^3 - 11x² + ab + b = 0 is divisible by x² - 4x -5 =0

Hence, making factors of it ,

x² - 4x - 5 = 0

x² - 5x + 1x - 5 = 0

x ( x - 5 ) + 1 ( x - 5 ) = 0

x + 1 ( x - 5 ) = 0

x = -1 , 5

Now subsequently we'll obtain two linear equivalents in " a " and " b "


Putting x = 5 , we obtain ,

-150 + ab + b = 0 and

Putting x = -1 , we obtain ,

-1 ( 11 + a ) + ab + b = 0

Now subtracting them and obtained equations will result in the values of a and b ,

-1 ( 11 + a ) = -150

a = 139

Similarly , b is also obtained aslike ,

-150 = - 140 ( b )

Hence , a = 139 and b = 15/14

★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★

Answer 2

Answer:

Given equation :

ax^3 - 11x² + ab + b = 0 is divisible by x² - 4x -5 =0

Hence, making factors of it ,

x² - 4x - 5 = 0

x² - 5x + 1x - 5 = 0

x ( x - 5 ) + 1 ( x - 5 ) = 0

x + 1 ( x - 5 ) = 0

x = -1 , 5

Now subsequently we'll obtain two linear equivalents in " a " and " b "

Putting x = 5 , we obtain ,

-150 + ab + b = 0 and

Putting x = -1 , we obtain ,

-1 ( 11 + a ) + ab + b = 0

Now subtracting them and obtained equations will result in the values of a and b ,

-1 ( 11 + a ) = -150

a = 139

Similarly , b is also obtained aslike ,

-150 = - 140 ( b )

Hence , a = 139 and b = 15/14

★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★