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The system of a quadratic equation and a linear equation may have how many intersection points?
Answer: The system of a quadratic equation and a linear equation can have either 0, 1, or 2 possible intersection points.
Let us go through the explanation to understand the solution.
The quadratic equation needs to be a parabola and a linear equation is a straight line, they may have at most two intersection points. It could also be possible for a straight line and a parabola to have no intersection point, a single point of intersection, but it is not possible to have more than 2 points of intersection.
There are three possible cases:
- No real solution (happens when they never intersect)
- One real solution (when the straight line just touches the quadratic)
- Two real solutions
The graph shows the three different possible solutions of a quadratic and a linear equation.
Therefore, the system of a quadratic equation and a linear equation can have either 0, 1, or 2 possible intersection points.