Real Solutions of Quadratic Equation

[nycmathguy]

How is 116 done?

 

[Country Boy]

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?

 

[nycmathguy]

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 \(x= \frac{-1\pm\sqrt{1- 4k^2}}{2k}\). 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 the \(\pm\)" 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.