Real Solutions of Quadratic Equation

How is 116 done?

 

Yes, those are all quadratic equation. Don't you know how to solve quadratic equations, by factoring, completing the square, or using the quadratic formula?

For example, number 113 says
"Find k such that that the equation kx^2+ x+ k= 0 has repeated real solutions."

The quadratic formula gives x= -1+/- sqrt(1- 4k^)/2k. A quadratic equation always has two roots (not necessarily different). In order that the two roots be the same the "discriminant", the quantity under the square root sign, must be 0 so that the "+/-" not give two different roots.
1- 4k^2= 0.

So what must k be?

 

1. I know how to solve quadratic equations.

2. Your LaTex did not display.

3. I always tell people if my questions are a pain in the neck, then simply move on.

4. If my ignorance is upsetting and frustrating, it is so easy to skip my threads and disappear.