26.In the xy-plane, the graph represented by y=x^2+px+r have how many intersects with axis-x?
1). p^2>r
2). r^2>p
1). p^2>r
2). r^2>p
An intersection with axis X is the equivalent of y = x^2+px+r = 0. This is a second degree equation, which could have from 0 to maximum two roots, depending on the discriminant, which will be p^2 - 4r.
Let me explain from the top with equations so that you may understand a bit better.
Second degree equations have the following pattern: a*x^2 + b*x + c = 0. The discriminant for these equations is called delta and is equal to b^2 - 4ac. Delta helps you to figure out how many solutions there are to your equation, meaning how many x-es fulfill a*x^2 + b*x + c = 0. You have three cases:
1. delta < 0 means that there is no x with a*x^2 + b*x + c = 0. Example: x^2 + 2x + 6 = 0 (in this case, the equation will always be positive).
2. delta = 0 means that there is just one x with a*x^2 + b*x + c = 0. Example: x^2 + 2x + 1 =0 (equivalent to (x+1)^2 = 0, giving you x = -1)
3. delta > 0 means that there are two x'es with a*x^2 + b*x + c = 0. Example: x^2 -6x +8 = 0 (equivalent to (x-4)(x-2) = 0, with x either 4 or 2).
Now let's get back to our problem.... We need to figure out if p^2 - 4r is smaller, greater than or equal to 0.
Stmt 1 doesn't shed light on whether p^2 is greater than 4r, just on whether p^2 is greater than r. So it is not sufficient by itself.
Stmt 2 is again insufficient by itself, largely for the same reason: you do not know the relationship between p^2 and 4r.
The two statements taken together do not help much either.
So my guess is E... Hope I'm not wrong, seeing as how my explanation is so long...
