Question

What js the discriminant of a cubic equation?

Answer 1

A parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax2 + bx + c = 0, the discriminant is b2 − 4ac; for acubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc − 4b3− 4a3c − 27c2.


hope this will help you

Answer 2

the discriminant of the general cubic equation

$a {x}^{3} + b {x}^{2} + cx + d = 0$

is given by:

$Δ = - 27 {a}^{2} {d}^{2} + 18abcd - 4 a{c}^{3} - 4 {b}^{3} d + {b}^{2} {c}^{2}$

As, every cubic is expressible in the form:

${y}^{3} + p y + q = 0$

By completing the cube and the line:

So, we can simplify the cubic discriminant as:

$Δ = - 27 {q}^{2} - 4 {p}^{3}$

The above simplified discriminant gives the same discriminant as for the general cubic equation. So, we can easily use this to find discriminant of any cubic equation.