Question

Jessica and Cameron have been solving systems of equations with one polynomial function of degree 2 or higher and one linear function. Jessica says there must always be two solutions, and Cameron says there will only be one solution. Using complete sentences, explain how Jessica can be correct, how Cameron can be correct, and how they both can be wrong.
@PhysicsGuru

Answer 1

@Compassionate

Answer 2

Well, a linear function is a line. A function degree two or more is at the very least a parabola. A parabola can be hit once (tangent) or twice. The way I imagine it, a cubic has to be hit at least twice. (parabola twice) (parabola once) and then a cubic twice or a cubic three times . Jessica could be correct if it were a parabola being intersected in the middle, and she could be right if it intersected the cubics at the bottom (twice.) Cameron could be correct if it intersected the parabola once.

They could both be wrong if the line and the parabola don't intersect, or if the cubic was intersected down the middle with three solutions. The higher you go up, the more solutions there will be, so it is pointless to continue going on with how many solutions there will be.