Quadratics and parabola

Algebra Level 4

For each positive integer n n , the parabola y = ( n 2 + n ) x 2 ( 2 n + 1 ) x + 1 y=(n^{2}+n)x^{2}-(2n+1)x+1 cuts the x axis at the points A n A_{n} and B n B_{n} .What is the value of n = 1 1992 A n B n \displaystyle \sum_{n=1}^{1992}A_{n}B_{n}

This problem is a part of my set Some JEE problems

1992 1991 \frac{1992}{1991} 1993 1992 \frac{1993}{1992} 1990 1991 \frac{1990}{1991} 1992 1993 \frac{1992}{1993} 1991 1992 \frac{1991}{1992}

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1 solution

Mayank Singh
Mar 11, 2015

Hint : You need the difference between the roots of the quadratic

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