itisSheldon wrote:

In x-y plane, does parabola y=\(ax^2\)+bx+c intersect to x-axis?

1) b= -2

2) c<0

In case of a parabola(quadratic expression) ax^2 + bx + c:

If parabola intersects x-axis at two distinct points, it means the quadratic expression has two distinct real roots, and this happens when (b^2 - 4ac) > 0

If parabola intersects x-axis at one point only, it means the quadratic expression has one real root, and this happens when (b^2 - 4ac) = 0

If parabola does not intersect x-axis at all, it means the quadratic expression has no real root, and this happens when (b^2 - 4ac) < 0

So we need to know the sign of (b^2 - 4ac).

Statement 1b is negative, but we don't know anything about a and c.

Not sufficient.

Statement 2c is negative, but we don't know anything about a and b.

Not sufficient.

Combining the two statements,

b and c are negative, but we don't know the sign of a.

If a is positive, then - 4ac will be positive, and then (b^2 - 4ac) will also be positive and the parabola will intersect x-axis.

If a is negative, then -4ac will be negative, and (b^2 - 4ac) could be either negative or positive or 0 depending on the magnitudes of a, b, c. So we cant say whether parabola will intersect x-axis or not.

So

not sufficient to determine.

Hence

E answer