Question

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QUESTION FOR TODAY #QUESTIONBANK#1
F(x)=$x^{4}$ -$2x^{3}$ +$3x^{2}$-ax+b leaves a remainder 5 and 19 on division by (x-1) and (x+1)respectively .Find The remainder when f(x) is divided by (x-2).
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Answer 1

Answer:

Step-by-step explanation:

x)=x4−2x3+3x2−ax+bf(x)=x4−2x3+3x2−ax+b

So , when it is divided by(x−1)(x−1) it’ll leave a remainder = f(1) = 5 (Given).

f(1)=14−2×13+3×12−a×1+b=5f(1)=14−2×13+3×12−a×1+b=5

=>1−2+3−a+b=5=>1−2+3−a+b=5

=>a−b=(−3)….Eqn(1)=>a−b=(−3)….Eqn(1)

Now , Similarly -

f(−1)=(−1)4−2×(−1)3+3×(−1)2−a×(−1)+b=19f(−1)=(−1)4−2×(−1)3+3×(−1)2−a×(−1)+b=19

=>1+2+3+a+b=19=>1+2+3+a+b=19

=>a+b=13….Eqn(2)=>a+b=13….Eqn(2)

Now , adding equations (1) and (2) , We’ll get -

(a+b)+(a−b)=(−3)+13(a+b)+(a−b)=(−3)+13

=>2a=10=>a=5=>2a=10=>a=5

So , (a+b)=13(a+b)=13 implies b=8b=8

Hence , Values of a and b are 5 and 8 respectively.