Category:Ferrari's Method
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This category contains pages concerning Ferrari's Method:
Let $P$ be the quartic equation:
- $a x^4 + b x^3 + c x^2 + d x + e = 0$
such that $a \ne 0$.
Then $P$ has solutions:
- $x = \dfrac {-p \pm \sqrt {p^2 - 8 q} } 4$
where:
| \(\ds p\) | \(=\) | \(\ds \dfrac b a \pm \sqrt {\dfrac {b^2} {a^2} - \dfrac {4 c} a + 4 y_1}\) | ||||||||||||
| \(\ds q\) | \(=\) | \(\ds y_1 \mp \sqrt { {y_1}^2 - \dfrac {4 e} a}\) |
where $y_1$ is a real solution to the cubic:
- $y^3 - \dfrac c a y^2 + \paren {\dfrac {b d} {a^2} - \dfrac {4 e} a} y + \paren {\dfrac {4 c e} {a^2} - \dfrac {b^2 e} {a^3} - \dfrac {d^2} {a^2} } = 0$
Ferrari's method is a technique for solving this quartic.
Source of Name
This entry was named for Lodovico Ferrari.
Pages in category "Ferrari's Method"
The following 2 pages are in this category, out of 2 total.