Help with quadratic equation please!!!

1. If (1-2k)x^2 + 8kx - (2+8k) = 0 has equal roots, find the value of k.

2. If x^2 + kx + 2x + 2k = 0has real and equal roots, find the value of k.

3. Find the value of p if the quadratic equation 3x^2 - 1 = 6x - 2p has real and equal roots.

p/s: please help me and show me how to solve these kind of problems. There are 2 unknowns. I will be sitting on the exam next week. Thanks for ur time!

1.
64 k ² = - 4 ( 1 - 2k ) ( 2 + 8 k )
64 k ² = - 4 ( 2 + 4k - 16 k ² )
64 k ² = - 8 - 16k + 64 k ²
16k = - 8
k = - 1/2

2.
x ² + (2k + 1 ) + 2k = 0
(2k + 1) ² = 8k
4k ² + 4k + 1 = 8k
4k ² - 4k + 1 = 0
( 2k - 1 ) ( 2k - 1 ) = 0
k = 1/2

3.
3 x ² - 6x + (2p - 1) = 0
36 = 12 (2p - 1 )
36 = 24p - 12
48 = 24p
p = 2

are u getting the answer the of this problem so u visit the link

http://math.tutorvista.com/algebra.html

http://en.wikipedia.org/wiki/College_alg…

(1).

discriminant = 0

b² - 4ac = 0

(8k)² - 4(1 - 2k)(-(2 + 8k)) = 0

16k + 8 = 0

k = -1/2

Alright so these are really easy to solve. I'm in Calc 151 in college right now so I know what I'm talking about LOL HAAHA ROFL LMAO HAHAHAHAHAHAHAH In class today we actually learned a really easy way to do this. We were taking the derivative of the f(x)=x and I was thinking. Man this is one tough problem. So I said, "Professor can you help me with this." He then came over and said, simple its 1. So now that I've said that let me tell you how this all correlates to your question. I then took the derivative on f(x)=2x and the answer was 3x^2-1=6x-2p which is exactly what your 3rd question is referring to! Isn't that an odd coincidence. Then I had to find out the answer to the equation using the quadratic equation. I knew this wasn't going to be easy. So I decided to have a study party that night to figure it out. We baked cookies first before we actually studied. The cookies were really really really really really really really really really really really really really really really really really really really really really tasty. After that we played xbox 360 and had a lot of fun. We then proceeded to answer the problem and study. We had a lot of fun and figured out some new things! It was great. I definitely wanna have more study parties more often. After that I went home and pondered about how I could apply this. The duck ate the clock as it twisted past the shepherds website with the bone in the cloud. After pondering I brushed my teeth and went to bed. Thats how my day was thanks for asking. How was yours? Did you enjoy it too?