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Find the value of a and …

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Find the value of a and b so that x^4 +x^3+ 8x^2 +ax+b is divible by x^2 +1.

    • Posted by Shivansh Handa 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    If {tex}x^4+x^3+8x^2+ax +b{/tex} is exactly divisible by x2 + 1, the remainder after division should be zero.
    Now let us perform long division

    We get, remainder = x (a - 1) + (b - 7)
     x (a - 1) + (b - 7 ) = 0
    {tex}\Rightarrow{/tex} x (a - 1) + (b - 7) = 0x + 0
    {tex}\Rightarrow{/tex} a - 1 = 0 and b - 7 = 0 [On equating the coefficients of like powers of x]
    {tex}\Rightarrow{/tex}a = 1 and b = 7

    0Thank You

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