1. discriminant

Please show this step by step and it'll be even better if there are some explanations for the solution!

Find the values of p for which the equation (1 - 2p)x^2 +8px - (2 + 8p) = 0 has one solution.

And hey, can you guys make up a question for me as well that's similar to this one?

2. read the section called Discriminant in the following article:

Quadratic equation - Wikipedia, the free encyclopedia

3. Originally Posted by delicate_tears
Please show this step by step and it'll be even better if there are some explanations for the solution!

Find the values of p for which the equation (1 - 2p)x^2 +8px - (2 + 8p) = 0 has one solution.

And hey, can you guys make up a question for me as well that's similar to this one? Mr F says: Surely your textbook has plenty of them ....?
$\displaystyle \Delta = (8p)^2 - 4(1 - 2p)(-(2 + 8p)) = 64 p^2 + 8(1 - 2p)(1 + 4p) = 16p + 8$.

4. Originally Posted by delicate_tears
Please show this step by step and it'll be even better if there are some explanations for the solution!

Find the values of p for which the equation (1 - 2p)x^2 +8px - (2 + 8p) = 0 has one solution.

And hey, can you guys make up a question for me as well that's similar to this one?

$\displaystyle x=\frac{-8p \pm \sqrt{64p^2 + 4(2 + 8p)(1 - 2p)}}{2-4p}$

We want that discriminant to be equal to zero.

$\displaystyle \sqrt{64p^2 + 4(2 + 8p)(1 - 2p)} = 0$
$\displaystyle 64p^2 + 4(2 + 8p)(1 - 2p) = 0$
$\displaystyle 64p^2 + 4(2 - 4p + 8p - 16p^2) = 0$
$\displaystyle 64p^2 + 8 +16p - 64p^2 = 0$
$\displaystyle 8 +16p= 0$
$\displaystyle 16p= -8$
$\displaystyle p= \frac{-1}{2}$

Plug p back into the original equation, and you will get your one solution for x.