Question

if f(x) =x⁴ -2x³ +3x²-ax +b is dimensions divided by (x-1) and (x+1), it leaves the remainders 5 & 19 respectively. find ‘a’ and ‘b’.​

Answer 1

x-1=0

or,x=1

f(1)=(1)⁴-2(1)³+3(1)²-a(1)+b=1-2+3-a+b=2-a+b

2-a+b=5

or,-a+b=3

x+1=0

or,x= -1

f(-1)=(-1)⁴-2(-1)³+3(-1)²-a(-1)+b=1+2+3+a+b=6+a+b

6+a+b=19

or,a+b=13

adding (1) and (2) equation we have

-a+b=3

a+b=13

2b=16

or,b=8

putting b=8 in 1 number equation

-a+8=3

or,-a= 3-8

or,-a= -5

or,a=5

therefore a=5 and b=8

Answer 2

Answer:

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