In high school, we learned that the roots of the quadratic equation are given by
Last week, a student asked me whether a similar formula exists for roots of a quartic equation. A quartic equation is an equation of degree four, which has four roots (a quadratic equation is of degree two, and therefore has two roots).
I told him yes, there is such formula, but there’s a reason why it is not taught in high school.
The roots of the quartic equation are given by the formula
No such formula exists for equations with degree 5 or higher, a fact that was proven by Norwegian mathematician Neils Henrik Abel in 1824 when he was only 22 years old (he discovered a proof three years earlier, but it was later found to contain an error). This theorem is known today as the Abel-Ruffini theorem.