Hi
I'm having trouble finding the roots of the equation below. While I have the final answer, I'm not sure how to arrive at that step-by-step. Any help would be appreciated.
x^2 + (z ln z - zb)x - (z^2 * b * ln z) = 0
The final answer has 2 roots in terms of 3 variables: x, b, z
Thanks in advance.
I did try this before posting but couldn't get anywhere near the final answer.
-(z ln z - zb) +/- sqrt{z ln z -zb) * (z ln z -zb) - 4z^2*b*ln z} / 2
-z ln z + zb +/- sqrt{z^2 (ln z)^2 - z^2*b*ln z - z^2*b*ln z + z^2*b^2 - 4 z^2*b*ln z} / 2
-z ln z + zb +/- sqrt{z^2(ln z)^2 - 6z^2*b*ln z + z^2*b^2} / 2
Final answer is:
(x - zb) (x + z ln z)
I don't see this simplifying to that, or at least I don't know how to do it.
Thanks
Maybe you should elaborate so the other person can actually see what they are doing wrong. Such a reply isn't very helpful - its been obvious from my all my posts that I've already to simplify it. I'm probably missing something, fine, but to keep saying "this simplifies" won't help me find my mistake.
[QUOTE=ForgotMath;643563]I did try this before posting but couldn't get anywhere near the final answer.
All right. A further hint on how to simplify the discriminant:
(Note that in my previous post a = z ln(z) and b = zb.)
This is of the form . So how do you simplify this further?
-Dan