I'm having trouble doing this question...

(3K-5)x^2+Kx+1=0

For what value of K will this quadratic equation have no real roots, one real root, or two real roots?

Answer as an inequality if necessary.

Question

I'm having trouble doing this question...

(3K-5)x^2+Kx+1=0

For what value of K will this quadratic equation have no real roots, one real root, or two real roots?

Answer as an inequality if necessary.

zehanz · Answer

This is a quadratic equation: ax²+bx+c=0.
The discriminant, D=b²-4ac tells you about the number of real roots:
D > 0: 2 real roots,
D = 0: 1 real root,
D < 0, no real roots.

You probably know all this already ;)

You just have to see that in your own equation a=3K-4, b=K and c=1.
Put these values for a, b and c in the formula for D and solve the above three cases for K.

anonymous · Answer

That's as far as I went.
As i was solving for no real roots i got stuck at this:
|dw:1359306176821:dw|