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Find the value of α and β , if the division of x2010+αx2011+β by (x−1) leaves the remainder zero and by (x+1) leaves the remainder 4. |
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Answer» Given polynomial p(x) = x2010 + αx2011 + β Now, as the remainder is zero when p(x) is divided by (x- 1). So put x = 1. (1)2010 + α(1)2011 + β = 0 1 + α + β = 0 α + β = -1.... (1) Similarly, put x = -1, In this case the remainder is 4 (-1)2010 + α(-1)2011 + β = 4 1 - α + β = 4 β - α = 3... (2) Adding (1) and (2) we get β = 1 and α = -2 |
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