Question

When the functions x²- ax +3 and 2a-x

are divided by x-b, the remainders are 1 and 4 respectively.
Find the values of a and b.

Answer 1

`a=3, b=2`

Explanation:

Using the remainder theorem,

`b^2-ab+3=1 \implies b^2-ab+2=0 \\ \\ 2a-b=4 \implies b=2a-4 \\ \\ \therefore (2a-4)^2-a(2a-4)+2=0 \\ \\ 4a^2+16-16a-2a^2+4a+2=0 \\ \\ 2a^2 - 12a+18=0 \\ \\ a^2-6a+9=0 \\ \\ (a-3)^2=0 \\ \\ a=3 \\ \\ \therefore 2(3)-b=4 \implies b=2`