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# Any Idea

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
1 year, 4 months ago

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

Hint: Ignore condition 1 for now. Staff · 1 year, 4 months ago

How? · 1 year, 4 months ago

There are $$b - 1$$ solutions in positive integers to $$a + c = b$$.

Sum over all possibilities of $$b$$.

Then, account for condition 1. Staff · 1 year, 4 months ago