Hi, please exlplain to me how the question 3 ( attached pdf) is worked out.. step by step. The answer we were told is
P=o
X=3

I'm VERY confused so please take it step by step and be as descriptive and clear as possible.

Thanks very much

Question 3: $x^2 - (p-2)x + 1 = p(x-2)$ is satisfied by only one value for $x$. What are the possible values of $p$?
If you simplify and collected like terms, it's a quadratic equation for $x$ with coefficients that involve $p$. Right?
Now, what do you know about real solutions to quadratic equations? Sometimes, there's two of them, sometimes there's one, and sometimes there are none. Right? OK - so what determines that? In particular, there's something about a quadratic that must be true in order that it have only one real solution. Write down that expression. Since that expression will involve the coefficients of the equation, and those coefficients involve $p$, the condition "this quadratic has exactly one real root" will translate into an equation for $p$. You can then solve it and then you'll have your answer to Question #3.