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Find the number of quadratic polynomials, \(ax^2 + bx + c\), which satisfy the following conditions :

(a) a,b,c are distinct;

(b) a,b,c \( \in \{1,2,3,...,1999\} \)

(c) \(x + 1\) divides \(ax^2 + bx + c\)

Note by Dev Sharma
2 years, 1 month ago

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Hint: You are asked to find sets that satisfy \( a - b + c = 0 \).

Hint: Ignore condition 1 for now.

Calvin Lin Staff - 2 years, 1 month ago

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How?

Dev Sharma - 2 years, 1 month ago

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There are \( b - 1 \) solutions in positive integers to \( a + c = b \).

Sum over all possibilities of \(b\).

Then, account for condition 1.

Calvin Lin Staff - 2 years, 1 month ago

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