Question

question 1 of 10
if the discriminant of an equation is negative, which of the following is true of
the equation?

a. it has two complex solutions.

b. it has two real solutions.

c. it has one real solution.

Explanation:

For a quadratic equation \( ax^{2}+bx + c = 0 \) (where \( a
eq0 \)), the discriminant is given by \( D=b^{2}-4ac \). The nature of the roots is determined by the discriminant:

• If \( D>0 \), the equation has two distinct real roots.
• If \( D = 0 \), the equation has one real root (a repeated root).
• If \( D<0 \) (negative discriminant), the roots are complex numbers (specifically, they are complex conjugates of the form \( m+ni \) and \( m - ni \)). So, a negative discriminant implies the equation has two complex solutions.

Answer:

A. It has two complex solutions.