1. ## Discriminants

What is the relationship between k, l and m in the quadratic equation: (k² +1²)x² + 2/(k + m)x + (l² + m²) = 0 to have equal roots?

Sorry but how exactly do I do this?

2. Originally Posted by xwrathbringerx
What is the relationship between k, l and m in the quadratic equation: (k² +1²)x² + 2/(k + m)x + (l² + m²) = 0 to have equal roots?

Sorry but how exactly do I do this?
If the roots are equal then they must be repeated. If they're repeated then the discriminant is equal to zero.

So get an expression for the discriminant and put it equal to zero. That will give the required relationship.

3. Ummm I get 2* k^2 * l^2 + 2 * l^2 * m^2 + 8 * l^2 * k * m^2 - 2 * k^2 * m^2 - 2 * l^4 = 0. Is that the relationship??

4. Originally Posted by xwrathbringerx
Ummm I get 2* k^2 * l^2 + 2 * l^2 * m^2 + 8 * l^2 * k * m^2 - 2 * k^2 * m^2 - 2 * l^4 = 0. Is that the relationship??
$\Delta = \left( \frac{2}{k + m}\right)^2 - 4 (k^2 + l^2) (l^2 + m^2) = 0$

5. I managed to get that ... but I expanded it and got that massive equation ... wat exactly am I meant to do afterwards?

6. Originally Posted by xwrathbringerx
I managed to get that ... but I expanded it and got that massive equation ... wat exactly am I meant to do afterwards?
Nothing. That's the relationship between k, l and m, as asked for.