Algebra Question #3

Algebra Level 4

If "r" or "s" are the roots of $x^{2} + A = 0$ and -100 < A < 100. Find $(r^2 - s^2)(r+s) / (r^2 + 2rs + s^2)(r-s)$ . Choices: $A. 1$ $B. -1$ $C. 1/A$

Algebra Question

A B C Not A, B, and C

2 solutions

Paul Ryan Longhas
Nov 21, 2014

x^{2} + A = 0 -----> r+s = 0. And (r^2 - s^2)(r+s) / (r^2 + 2rs + s^2)(r-s) = (r+s)(r+s)(r-s) / (r+s)(r+s)(r-s) = (0)(0)(r-s) / (0)(0)(r-s) = indeterminate

Nice problem.I just went typo or what is called blindly put factorise and cancel.My bad!

Raven Herd - 6 years, 3 months ago

William Isoroku
Jan 12, 2015

By vieta's formula the sum of the roots of a quadratic equation is $\frac{-b}{a}$ . This case, $b=0$ so the entire numerator is $0$ so the expression is $\boxed{0}$

Algebra Question #3

2 solutions

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