Q: What triangle cases may have one two or zero solutions?

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It may be called a singularity.

A point outside the triangle may.

The orthocenter of a triangle may lie outside the triangle since the ___altitude___ may not intersect any side of the triangle. * * * * * No. One of the altitudes must intersect the side opposite it and so it is not correct to say ANY side of the triangle.

The orthocenter may fall outside of a triangle. The orthocenter usually lies within the inside the triangle. However this is only the case if the triangle is acute.

No. By definition, a quadratic equation can have at most two solutions. For a quadratic of the form ax^2 + bx + c, when the discriminant of a quadratic, b^2 - 4a*c is positive you have two distinct real solutions. As the discriminant becomes smaller, the two solutions move closer together. When the discriminant becomes zero, the two solutions coincide which may also be considered a quadratic with only one solution. When the discriminant is negative, there are no real solutions but there will be two complex solutions - that is those involving i = sqrt(-1).

Related questions

It may be called a singularity.

In catatonic stupor, motor activity may be reduced to zero.

The orthocenter of a triangle may lie outside the triangle because an altitude does not necessarily intersect the sides of the triangle.

True for an obtuse triangle!

Only if its in the form of an equilateral triangle or a isosceles triangle will it have lines of symmetry.

yes

A point outside the triangle may.

No, compounds are not solutions. Solutions may contain compounds, but they are not the same thing.

velocity may be zero or may not be zero i.e. if the object may continue to move with uniform velocity.

velocity may be zero or may not be zero i.e. if the object may continue to move with uniform velocity.

The orthocenter of a triangle may lie outside the triangle since the ___altitude___ may not intersect any side of the triangle. * * * * * No. One of the altitudes must intersect the side opposite it and so it is not correct to say ANY side of the triangle.

The variable term, X^3, is a third order polynomial term and will render three solutions, though one of those may be zero.