Final answer:
A quadratic equation can have only one real number root if the discriminant is zero. It can have only one imaginary root if the discriminant is negative.
Step-by-step explanation:
A quadratic equation can have only one real number root if the discriminant (the value inside the square root in the quadratic formula) is equal to zero. This means that the quadratic equation has a repeated root, or in other words, the parabola represented by the equation touches the x-axis at only one point. For example, the quadratic equation x^2 - 6x + 9 = 0 has only one real number root, which is x = 3.
A quadratic equation can have only one imaginary root if the discriminant is negative. In this case, the square root in the quadratic formula will be an imaginary number, and there will be no real number solutions. For example, the quadratic equation x^2 + 4 = 0 has only one imaginary root, which is x = 2i.