The value of ab so that x4 + x + 8x...
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The value of ab so that x4 + x + 8x2 + ax + b is divisible by x2 + 1, is

JEE/Engineering Exams
Maths
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Ans: If ( x^{4}+x^{3}+8 x^{2}+a x+b ) is exactly divisible by ( x^{2}+1, ) then the remainder should be zero. On dividing the polynomial by ( x^{2}+1, ) we get, [ begin{array}{c} left.x^{2}+1right) x^{4}+x^{3}+8 x^{2}+a x+bleft(x^{2}+x+7right. x^{4}+x^{2} =frac{-}{x^{3}+7 x^{2}+a x+b} x^{3}+x+x frac{-x^{3}-x^{2}+x(a-1)+b}{7 x^{2}}+7 -frac{7 x^{2}}{x(a-1)+b-7} end{array} ]
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