Question 173956
1) Look at the value of the discrimenent. Then you can see if there are 0, 1 or 2
2) If you are given roots, then you can 'recreate' the eqaution as follows
y = (x - X1)(x - X2)  sub in the roots for X1 and X2, then expand the equation
3) Sure, imagine a parabola that intersects the x axis in two places. Now imagine a different parabola, with the same two intercepts but a more or less steep curve and a vertex higher of lower.

Easier to draw it than describe it.
Layout a coordinate plane
Pick two points on the x axis
pick a vertex below the x axis
Draw the parabola that connects all three of those points.
Now, move the vertex point twice as far below the x axis as the first vertex.
Now, draw the parabola that contains the new vertex and the 2 roots on the x axis.

Now ou see two different curves with the same roots.