Step-by-step explanation:
Given that:-
[tex](2x - 1)[/tex]
is exactly divisible by
[tex]6 {x}^{2} + ax - 4[/tex]
and
[tex]b {x}^{2} - 11x + 3[/tex]
We need to simply, place the value of x.
[tex]2x - 1 = 0[/tex]
[tex]2x = 1[/tex]
[tex]x = \frac{1}{2} [/tex]
Now,
[tex]6 {( \frac{1}{2} )}^{2} + \frac{a}{2} - 4 = 0[/tex]
[tex] \frac{3 + a}{2} = 4[/tex]
[tex]3 + a = 4 \times 2 = 8[/tex]
[tex]a = 8 - 3[/tex]
[tex]a = 5[/tex]
Now, to find b.
[tex]b {( \frac{1}{2}) }^{2} - \frac{11}{2} + 3 = 0[/tex]
[tex] \frac{b}{4} - \frac{11}{2} = - 3[/tex]
[tex] \frac{b - 22}{4} = - 3[/tex]
[tex]b - 22 = - 12[/tex]
[tex]b = 10[/tex]
is the answer.
Now, we need
[tex] {b}^{2} - {a}^{2} + a - b[/tex]
[tex]100 - 25 + 100 + 5[/tex]
[tex] = 205 - 25[/tex]
[tex] = 180[/tex]
is the answer.
Hope it helps :D
