In this video I go over the first step in deriving the Cubic Formula, which is to eliminate the x2 term from the Cubic Equation by using the PQ Substitution method. This allows us to later apply Vieta's substitution to obtain a quadratic formula, which we can solve. As in the PQ Quadratic Formula method, I set x = y + k and then expand the powers and select a k value such that the x2 terms get eliminated. Then rearranging and defining p and q as the terms for the coefficients of the x1 and x0, we obtain the PQ version of the Cubic Equation.
Notes: Step 1: Get rid of x2 term using PQ Substitution
Written notes — mirrored from Cubic Formula Proof, which walks through the complete derivation.
Just as in the PQ substitution method for the quadratic equation, we would like to get rid of the x2 term from the cubic function:
ax3 + bx2 + cx + d = 0
It's possible to solve the equation y3 + py + q = 0 by applying Vieta's substitution to obtain a quadratic formula:
Let's now apply the PQ substitution method to the cubic function.
- Watch on: 3Speak · YouTube · Telegram
- Full written notes: Cubic Formula Proof
- Playlist: Cubic Formula Proof YouTube playlist
- More math: mes.fm/math
Originally posted on the Hive blockchain →