solve 6. part
plz solve in steps
Answers
The remainder coems out to be 10
Hope it helps! ^_^
Answer:
Remainder is 8.5 when polynomial is divided by x-2
Step-by-step explanation:
Given
f(x) = x^4 - 2x³ + 3x²-ax+b
On dividing with x-1 it leaves remainder 5
So,
f(x) = x^4 - 2x³ + 3x²-ax+b
f(1) = (1)^4 - 2(1)³ + 3(1)²-a(1)+b = 5
1-2+3-a+b = 5
-1+3-a+b = 5
b-a+2 = 5
b-a =5-3
b-a = 2....................i
On dividing with x+1 it leaves remainder 19.
x+1 = 0
x = -1
Put x= -1
f(x) = x^4 - 2 x³ + 3 x²-ax+b
f(-1) = (-1)^4 - 2(-1)³ + 3(-1)²-a(-1)+b
19 = 1-2(-1)+3+a+b
19 =1+2+3+a+b
a+b = 19 - 6
a+ b = 13.....................ii
On adding i and ii
we get,
2 b = 15
b= 15/2
a= 11/2
Hence the equation is x^4 - 2x³ + 3x²-11/2x+15/2
f(x) = x^4 - 2x³ + 3x²-11/2x+15/2
Remainder when divided by x-2, so put x=2
f(2) = (2)^4 - 2(2)³ + 3(2)²-11/2(2)+15/2
= 16- 16 + 12 -11+ 15/2
= 1+ 15/2
= 17/2
= 8.5
Hence the remainder is 8.5 polynomial when divided by x-2