Assignment 32
Here is an example showing how one can logically solve an algebraic inequality:
============================== Returning to quadratic equations, here is a TI-83 program that will produce real number solutions for the quadratic equation Ax^{2}+Bx+C = 0 if you input values for A, B, and C. This program does not identify complex number roots.
Problem: Solve x^{2} - 7x < 0. Solution (with communication): x^{2 }- 7x < 0 ==> x(x - 7) < 0. Since x - 7 is less than x, the only way the conditional statement can be true is if x - 7 < 0 or x > 0 ==> x < 7 or x > 0. In other words, the conditional statement is true if x < 7 or if x > 0. Problem: Describe the solution set defined by x^{2} - 4 > 0 and 4 - x^{2} < 0 Solution (with communication): Graph the parabolas y = x^{2} - 4 and y = 4 - x^{2}. The requested solution set is all points above the parabola y = x^{2} - 4 and below the parabola y = 4 - x^{2}. |