What is the maximum number of real solutions a quadratic equation can have?

What is the maximum number of real solutions a quadratic equation can have?

• A. 0
• B. 1
• C. 3
• D. 2

Answer: (D)

The graph of a quadratic is a parabola, which can cross the x-axis at most twice. For an equation of the form ax^2 + bx + c = 0 with a ≠ 0, that means there are at most two real solutions. If the discriminant b^2 − 4ac is positive, you get two distinct real solutions; if it’s zero, you get one real solution (a repeated root); if it’s negative, there are no real solutions. Since we’re looking for the maximum number of real solutions, a quadratic can have two.

The graph of a quadratic is a parabola, which can cross the x-axis at most twice. For an equation of the form ax^2 + bx + c = 0 with a ≠ 0, that means there are at most two real solutions. If the discriminant b^2 − 4ac is positive, you get two distinct real solutions; if it’s zero, you get one real solution (a repeated root); if it’s negative, there are no real solutions. Since we’re looking for the maximum number of real solutions, a quadratic can have two.