Question 1

Can a quadratic equation have three roots?

Accepted Answer

No. According to the Fundamental Theorem of Algebra, a polynomial equation of degree n has exactly n complex roots. A quadratic equation is a second-degree polynomial (n = 2) and thus can have at most two roots.

Question 2

What are imaginary roots?

Accepted Answer

When the discriminant D = b² - 4ac is negative, the square root term contains a negative value, yielding roots with the imaginary unit i (where i = √-1). These are complex numbers representing points where the parabola does not cross the x-axis.

Chapter 9: Vector Algebra

Scalar Dot Product