0

I sort of doubt there is a good one out there, but I thought I'd ask. I'm looking for a mnemonic for the general discriminant of the polynomial $ax^3+bx^2+cx+d$, which is

$$b^2c^2-4ac^3-4b^3d-27a^2d^2+18abcd$$

Obviously if necessary, one can use different letters and / or assume a=1. However, the expression is homogeneous with respect to the coefficients, so it might be easier to leave $a$ in.

A much easier case is the discriminant of $x^3+px+q$, which has discriminant $-4p^3-27q^2$.

pancini
  • 19,216
  • Not a mnemonic, but a different way to approach the cubic: http://nickalls.org/dick/papers/maths/cubic1993.pdf – Andy Walls Dec 07 '18 at 02:13

1 Answers1

1

I don't have a nnemonic to suggest. However, after my sixth grade gym teacher made us write down our locker combination and the serial number on the back 200 times on the first day of school, I have never forgotten either. I still use the lock and I'm in my forties.

Bill
  • 39