Question 134718
1) Look at the determinant part of the quadratic equation
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
The determinant is 
{{{sqrt( b^2-4*a*c )) }}} 
If that results in a negative == no solutions (complex numbers)
If it is positive, then two roots
If it is 0, the one root two times

2) Lets say the solutions are x=5 and x= 7
Then {{{(x-5)(x-7) = 0 }}} will give a quadratic equation with those solutions
More generally, if the roots are a and b
{{{(x-a)(x-b) = 0 }}} then just multiply it out 

3)Sure. One quick way to see that is to just multiply by a constant C
{{{C(x-a)(x-b) = 0 }}} same root, different equation

make sense?