when a polynomial p(x) =x^4-2x^3+3x^2-ax +b is divisible by x-1 and x+1 , the reminder are 5 and 19 respectively . find the remainder when p(x) is divided by x-2.
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Answer:
9
Step-by-step explanation:
on putting x= 1
1⁴-2×1³+3×1²-a×1+b
= 2-a+b= 5....,..........,...(remainder)
=> --a+b= 3...........(1)
on putting x= -1
(-1)⁴-2(-1)³+3(-1)²-a(-1)+b
= -1+2+3+a+b
= 4+a+b = 19......,....,. .(remainder)
=> a+b= 15.........(2)
on solving by (1) and (2)
a= 6
b= 9
substituting a and b in p(x)
x⁴-2x³+3x²-6x+9..............(3)
putting x= 2 in (3)
2⁴+2×2³+3×2²-6×2+9
= 16-16+12-12+9
= 9
therefore p(x) when divident by x-2 the
remainder= 9
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