Question

A quadratic equation could have the following number of solutions except?

a) none
b) 1
c) 2
d) 3

Answer 1

A quadratic equation may have zero, one, or two solutions, but never three; the number of solutions is determined by the discriminant of the quadratic formula.

Step-by-step explanation:

The quadratic equation is represented by the form ax² + bx + c = 0, and its solutions can be found using the quadratic formula. According to the fundamental theorem of algebra, a quadratic equation has at most two solutions. These solutions depend on the discriminant (b² - 4ac). If the discriminant is positive, there are two distinct real solutions. If it is zero, there is one unique solution. If the discriminant is negative, there are two complex solutions.

Therefore, a quadratic equation could have the following number of solutions: none (in the real number system), one, or two, but never three.