Question

x²- ax³ + bx² "-cx" +8 =0 divided by (x-1) leaves a remainder of 4 divided by (x+1) leaves a remainder 3 then b =​

Answer 1

in this question we use

remainder theorem

x⁴-ax³+bx²-cx+8=p(x).(x-1)+4

Where p(x) be a cubic polynomial.

Since we do not know p(x) to eliminate it put x=1 which makes p(x).(x-1)=0

Then,

1-a+b-c+8=4

So -a+b-c=-5 …. let it be equation 1

Similarly

x⁴-ax³+bx²-cx+8=q(x).(x+1)+3

Put x=-1

1+a+b+c+8=3

a+b+c=-6 .let it be equation 2

Adding equations 1 and 2

We get

2b=-11

So b=-11/2 which is the required solution..