Quadratic equations

Can you provide an example of
different quadratic equations which gives the same solutions? What is the
general rule that allows you to see that 2 different quadratic have the same
solutions?
Many of you showed that if two real numbers a and b are solutions for a
quadratic equation. The quadratic equation can be the form of (X-a)(X-b)=0.
What if a and b are negative numbers? Can you give an example of a quadratic
equation with -5 and -3 as its solutions?
How do you know if a quadratic equation will have one, two, or no solutions?
How do you find a quadratic equation if you are only given the solution? Is it
possible to have different quadratic equations with the same solution? Explain,
then provide one or two solutions with in which someone can create a quadratic
equation.
Quadratic equations may be solved by graphing, using the quadratic formula,
completing the square, and factoring. What are the pros and cons of each of
these methods? When might each method be most appropriate? Which method do you
prefer? Explain why.