In this video I go over the second step in deriving the Cubic Formula, and this involves converting our earlier PQ version of the cubic formula into a quadratic formula using Vieta's substitution. In step 1 we converted x into y by the equation x = y + k. In step 2 we convert y into z by the equation y = z + k/z. Then we do the exact same procedure as before to select a k value that cancels out the z1 terms. Then, multiplying by z3 we obtain a quadratic equation, which we can solve using the PQ version of the quadratic formula. In later steps, we will convert z back into y and then finally back into x.
Notes: Step 2: Solve y3 + py + q = 0 using Vieta's Substitution
Written notes — mirrored from Cubic Formula Proof, which walks through the complete derivation.
Now we can apply Vieta's substitution to transform our PQ cubic equation into a quadratic equation.
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- Full written notes: Cubic Formula Proof
- Playlist: Cubic Formula Proof YouTube playlist
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