Question

if (2x minus 1) is exactly divisible by 6 X square + ax - 4 and b x square - 11x + 3, then the value of b square minus a square + a minus b is​

Answer 1

Explanation:

Given that:-

`(2x - 1)`

is exactly divisible by

`6 {x}^(2) + ax - 4`

and

`b {x}^(2) - 11x + 3`

We need to simply, place the value of x.

`2x - 1 = 0`

`2x = 1`

`x = (1)/(2)`

Now,

`6 {( (1)/(2) )}^(2) + (a)/(2) - 4 = 0`

`(3 + a)/(2) = 4`

`3 + a = 4 * 2 = 8`

`a = 8 - 3`

`a = 5`

Now, to find b.

`b {( (1)/(2)) }^(2) - (11)/(2) + 3 = 0`

`(b)/(4) - (11)/(2) = - 3`

`(b - 22)/(4) = - 3`

`b - 22 = - 12`

`b = 10`

is the answer.

Now, we need

`{b}^(2) - {a}^(2) + a - b`

`100 - 25 + 100 + 5`

`= 205 - 25`

`= 180`

is the answer.

Hope it helps :D