Question

1. x² - ax ³+ bx²- cx + 8 = 0 divided by (x - 1) leaves a remainder of 4, divided by (x + 1) leaves a remainder 3. then b =


(a) 2.5
(b) -5.5
(c) 3.5
(d) 6.5

plz let me know the explanation ​

Answer 1

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..

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