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The first formula found for solving cubic equations applied only to cubics without a square term. In modern notation, these look like x³ + px + q = 0. These are sometimes called "depressed cubics." Let y = x - and substitute in the equation below to "reduce" the cubic. Verify that the square term will disappear. y³ + ay² +by+c=0

The first formula found for solving cubic equations applied only to cubics without a square term. In modern notation, these look like x³ + px + q = 0. These are sometimes called "depressed cubics." Let y = x - and substitute in the equation below to "reduce" the cubic. Verify that the square term will disappear. y³ + ay² +by+c=0

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.4: Graphs Of Quadratic Equations: The Discriminant
Problem 1CE
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The first formula found for solving cubic equations applied only to cubics without a square term. In modern notation, these look like x³ + px + q = 0. These are sometimes called "depressed cubics." Let y = x - and substitute in the equation below to “reduce” the cubic. Verify that the square term will disappear. y³ + ay² +by+c=0 Now we can solve this equation for x using the formula for x, and then subtract to find y.
Transcribed Image Text:The first formula found for solving cubic equations applied only to cubics without a square term. In modern notation, these look like x³ + px + q = 0. These are sometimes called "depressed cubics." Let y = x - and substitute in the equation below to “reduce” the cubic. Verify that the square term will disappear. y³ + ay² +by+c=0 Now we can solve this equation for x using the formula for x, and then subtract to find y.
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