Discriminant of a quadratic equation in 2 variables

[Ashu2912]

Can anyone tell me how to calculate the discriminant of a general equation of 2 degree in 2 variables, ax$^{2}$+by$^{2}$+2gx+2fy+2hxy+c=0? Thanks!

 

[Stephen Tashi]

I've never seen a textbook that defined the descriminant for a polynomial of two variables. How do your materials define it?

 

[Ashu2912]

In my text it is defined as abc+2gfh-a(f sq.)-b(g sq.)-c(h sq.). I just want to know how is it derived and what is it's significance and implication...

 

[Stephen Tashi]

What is the title of your text?

Wolfram has a page on the discriminant of a quadratic curve and it gives a different formula:
http://mathworld.wolfram.com/QuadraticCurveDiscriminant.html

 

[blue_raver22]

The discriminant of a quadratic equation in 2 variables is a mathematical term that represents the nature of the roots of the equation. In the general equation of 2 degrees in 2 variables, ax^{2}+by^{2}+2gx+2fy+2hxy+c=0, the discriminant can be calculated using the following formula: b^{2}-4ac-4h^{2}. This formula involves the coefficients of the equation, a, b, c, g, f, and h.

To calculate the discriminant, substitute the values of these coefficients into the formula and simplify the expression. The resulting value will determine the nature of the roots of the equation. If the discriminant is positive, the equation will have two distinct real roots. If the discriminant is zero, the equation will have one real root. And if the discriminant is negative, the equation will have two complex roots.

The discriminant is an important factor in understanding the behavior of quadratic equations in 2 variables. It helps determine the number and type of solutions the equation will have, which can have significant implications in various scientific and mathematical applications.