Can someone please help me with this confusing math problem on discriminant and quadratic inequalities?
I think I'm doing it all wrong...
It says:
Find the range or ranges of values k can take for kx^2-4x+5-k=0 to have real roots.
So I did this:
a=k
b=-4
c=5-k
(-4^2) -4(k)(5-k)>= (greater than or equal to) 0
16-20k+4k^2>=o
Then I subtracted 16.
4k^2-20k>=-16
then I didn't know what to do! i thought maybe I could factor the 4 out like this:
4k(k-5)>=-16
or should I just divide everything by 4 like this:
K^2-5k>=-4
and then factor the k out like this
k(k-5)>=-4
But then I'm stuck with what to do from here.
If I added 5 to both sides I would get
k(k)>=1
and then would I factor the k back in and get
k^2>=1
k>= -1 or =1?
Would that be the answer or am I completely way off?