Without solving, determine the character of the solutions of the equation.
-$$x ^ { 2 } + 4 x + 5 = 0$$
A) two unequal real solutions
B) two complex solutions that are conjugates of each other
C) a repeated real solution

Question

Quizplus · Accepted Answer

The discriminant of the quadratic equation $ax^2 + bx + c = 0$ is given by $D = b^2 - 4ac$. For the given equation, $a = 1$, $b = 4$, and $c = 5$, so $D = 4^2 - 4(1)(5) = 16 - 20 = -4$. Since $D < 0$, the equation has two complex solutions that are conjugates of each other.

Without Solving, Determine the Character of the Solutions of the Equation