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Answers
10
f(x) = x^4 - 2x^3 +3x^2 - ax + b
f(x) is divided by (x -1) & remainder is 5
i.e., f(1) = 5 ( (Remainder theorem)
1^4 - 2(1)^3 +3(1)^2 - a(1) + b = 5
i.e,. -a + b = 3.....(1)
f(x) is divided by (x +1) & remainder is 19
i.e., f(-1) = 19 ( (Remainder theorem)
(-1)^4 - 2(-1)^3 +3(-1)^2 - a(-1) + b = 19
a + b = 13.....(2)
now from (1) & (2)...
a = 5 ; b = 8
therefore....
f(x) = x^4 - 2x^3 +3x^2 - 5x + 8
again f(x) is divided by (x -2) & then the remainder is....
f(2) ( Remainder theorem)
means...
2^4 - 2(2)^3 +3(2)^2 - 5(2) + 8 = 10
hence the remainder = 10
Answer:hello friends
Step-by-step explanation:if f(x) = x^4-2x^3 + 3x^2-ax+b is divided by (x+1) and got the remainder 5
Then f(1)=5
1^4-2×1^3+3×1^2-a×1+b
=5
That is -a+b=3_(1)
If it is divided by (x+1) and got the remainder 19
That is =19
-1^4-2×-1^3+3×-1^2-a×-1 +b
=19
A+B=. 13_(2)
From 1 and 2 we get a =5 ,b =8
Then , if f(x) is divided by x-2 then f(2) then
The remainder is 10
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