Waste less time on Facebook — follow Brilliant.
×

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

No vote yet
1 vote

Comments

Sort by:

Top Newest

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

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

Log in to reply

@Calvin Lin How? Dev Sharma · 1 year, 4 months ago

Log in to reply

@Dev Sharma 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 · 1 year, 4 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...