SOLUTION: Find the number k for which the quadratic equation x^2+kx+k=0 has no real solutions. (Hint: use the quadratic formula to get a polynomial inequality in the variable k, which then y

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the number k for which the quadratic equation x^2+kx+k=0 has no real solutions. (Hint: use the quadratic formula to get a polynomial inequality in the variable k, which then y      Log On


   

Question 865063: Find the number k for which the quadratic equation x^2+kx+k=0 has no real solutions. (Hint: use the quadratic formula to get a polynomial inequality in the variable k, which then you can solve.)
Steps to solve
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe putting attention on the discriminant is more efficient.
D=%28-k%29%5E2-4%2Ak=k%5E2-4k.

You want no real solutions, so this means D%3C0.
highlight_green%28k%5E2-4k%3C0%29, and you want to know the solutions to this for k.
k%28k-4%29%3C0
Critical points are 0 and 4. If you cannot accept this logically, then you need help specifically for this.

Assuming you know how to accept those critical points for k, you can test intervals which those critical points make on the k number line.
-
Interval k%3C0, example point k=-1.
k(k-4)=(-)(-)=(+)>0
This interval does not work.
-
Interval 0%3Ck%3C4, example point k=1.
k(k-4)=(+)(-)=(-)<0
THIS interval WORKS.
-
Interval 4%3Ck, example point k=5.
k(k-4)=(+)(+)>0
This interval does not work.

SOLUTION: highlight%28highlight%280%3Ck%3C4%29%29.