![]() It was only later that people came up with the concepts of negative numbers, zero and even more esoteric concepts like imaginary numbers - the square roots of negative numbers. Loh delved into mathematics history to find that the Babylonians and Greeks had the same insights, although their understanding was limited because their math was limited to positive numbers. Loh’s version is easier for students because it, “provides one method for solving all kinds of quadratic equations.” A technique with ancient rootsĭr. “Math is not about memorizing formulas without meaning, but rather about learning how to reason logically through precise statements,” Dr. Guessing also becomes cumbersome for quadratics with large numbers, and it only works neatly for problems that are contrived to have integer answers. “The fact that you suddenly have to switch into a guessing mode makes you feel like maybe math is confusing or not systematic,” Dr. ![]() If they exist, then r and s are the two and only two solutions.įiguring out the factors that work is essentially trial and error. The key is to find r and s such that the sum of r and s equals 4 (that is, r + s = 4), and multiplying r and s produces –5 ( r × s = –5). Multiplying out ( x – r)( x – s) produces x² – ( r + s) x + rs. That is, you hoped to find two numbers r and s such that x² – 4 x – 5 = ( x – r)( x – s) = 0 You might recall your teacher asking you to factor the jumble of symbols. ![]() For simplicity, we’ll consider an equation where a = 1. Before students are presented with the quadratic formula, they’re taught a simpler method to solve certain equations.
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