A quadratic equation can have how many real solutions at most?

A quadratic equation can have how many real solutions at most?

• A. Three
• B. Two
• C. One
• D. Zero

Answer: (B)

Quadratics form a parabola, and a parabola can intersect the x-axis in at most two points. That means the largest possible number of real solutions is two. If the discriminant is positive, there are two distinct real solutions; if it’s zero, there is exactly one real solution; if it’s negative, there are no real solutions. So two is the greatest number of real solutions a quadratic can have.

Quadratics form a parabola, and a parabola can intersect the x-axis in at most two points. That means the largest possible number of real solutions is two. If the discriminant is positive, there are two distinct real solutions; if it’s zero, there is exactly one real solution; if it’s negative, there are no real solutions. So two is the greatest number of real solutions a quadratic can have.