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Let rbe a real number andn in N be such that the polynomial 2x^(2)+ 2x + 1dividesthe polynomial (x + 1)^(n) - r. Then (n,r)can be-(A)(4000, 4^(1000)) (B)(4000, 1/4^(1000)) (C)(4^(1000),1/4^1000) (D)(4000,1/4000) |
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Answer» `(4000, 4^(1000))` `X = (-1+i)/(2), (-1-i)/(2)` x satisfies `(x + 1)^(N) - r = 0` `((-1+-i)/(2) + 1)^(n) - r = 0` `((1+-i)/(2))^(n) -r = 0` `((1)/(sqrt(2)))^(n) ((1+i)/(sqrt(2)))^(n) = r` `((1)/(sqrt(2)))^(n)(e^(+-( IPI)/(4)))^(n)= r` RHS= real LHS = realonly when n = multiply of 4 `n = 4000` `r = ((1)/(sqrt(2)))^(4000) = 1/(4^(1000))` |
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