Quadratic equations can be written in the form ax^2 + bx + c = 0. What is the maximum number of roots that a quadratic equation can have? A. one B. two C. three D. four
Answer (1)
A quadratic equation is represented in the standard form a x 2 + b x + c = 0 , where a , b , and c are constants, and a = 0 . The maximum number of roots, or solutions, that a quadratic equation can have is determined by its degree.
A quadratic equation is of degree 2 because the highest power of the variable x is 2. According to the Fundamental Theorem of Algebra, a polynomial equation of degree n can have a maximum of n roots. Therefore, a quadratic equation can have a maximum of 2 roots.
These roots can be:
Real and Distinct : When the discriminant 0"> b 2 − 4 a c > 0 , the equation has two distinct real roots.
Real and Equal : When the discriminant b 2 − 4 a c = 0 , the equation has exactly one real root that is repeated.
Complex Conjugates : When the discriminant b 2 − 4 a c < 0 , the equation has two complex roots which are not real.
Thus, the correct answer to the question is B. two .
