Question

A student claims that a linear-quadratic system of equations has three solutions. Explain the error the student made.

Answer 1

Explanation:

A line and a quadratic (parabola) can have either 0, 1, or 2 solutions.

• 0 solutions: the line and quadratic do not intersect.
• 1 solution: the line and quadratic are tangent (intersect at one point), or the line is the axis of symmetry (intersects only at the vertex).
• 2 solutions: the line and quadratic intersect at two points.

It is impossible for a linear-quadratic system to have more than 2 solutions.