Find the values of a and b so that x^4+x^3+8x^2+ax-b is divisible by (x^2+1) pls help me
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x^2+1=0
x^2=-1=i^2
x=+/-i
Put x=+i , R=i^4+i^3+8i^2+ai+b=0
1-i-8+ai+b=0
(a-1).i+b=7…………………(1)
Put x=-i
R=(-i)^4+(-i)^3+8(-i)^2-ai+b=0
1-i^3+8i^2-ai+b=0
1+i-8-ai+b=0
(1-a)i+b=7……………………..(2)
Subtract eq.(2)from (1)
2(a-1).i=0
2 and i does not equal zero,
(a-1)=0
a=1 , put a=1 in eq.(1)
b=7
a=1 ,b=7 , Answer...
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