Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the
equation.
-$$x ^ { 2 } - 4 x + 5 = 0$$
A)two real solutions
B)two nonreal solutions
C)exactly one real solution

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the equation $x^2 - 4x + 5 = 0$, the discriminant is $(-4)^2 - 4(1)(5) = 16 - 20 = -4$. Since the discriminant is negative, the equation has two nonreal (complex) solutions.

Use the Discriminant to Determine the Number and Nature of the Solutions