Question

let a and b be the remainder when polynomial y ^3 +2y^2-5ay-7&y^3 +ay^2-12y+6are divided by y+1 and y-2 respectively if 2a +b=6 find value of a.

Answer 1

hope it helps you.......

Answer 2

Answer:

a=2

Step-by-step explanation:

Let p(y) = y3 + 2y2 - 5ay - 7 and q(y) = y3 + ay2 - 12y + 6 be the given polynomials.

Now, A = Remainder when p(y) is divided by (y + 1)

=> A = p (-1)  =>A = (-1)3 + 2(-1)2 - 5a(-1) - 7 [p(y) = y3 + 2y2 - 5y - 7]

=> A = -1 + 2 + 5a - 7   => A = 5a - 6

And B = Remainder when q(y) is divided (y - 2)

=> B = q(2)  =>B = (2)3 + a(2)2 - 12 × 2 + 6 [q(y) = y3 + ay2 - 12y + 6]

=>B = 8 + 4a - 24 + 6   => B = 4a - 10

Substituting the values of A and B is 2A + B = 6, we get

2(5a - 6) + (4a - 10) = 6

=> 10a - 12 + 4a - 10 =6

=> 14a - 22 = 6

=14a=28

=a=28/14

a=2