Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex.
-$w ^ { 2 } + 4 w + 5 = 0$
A) Two distinct irrational solutions
B) Two distinct rational solutions
C) One rational solution (a double solution)
D) Two distinct nonreal complex solutions

Question

Quizplus · Accepted Answer

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

Evaluate the Discriminant for the Equation w2+4w+5=0w ^ { 2 } + 4 w + 5 = 0w2+4w+5=0

Evaluate the Discriminant for the Equation $w ^ { 2 } + 4 w + 5 = 0$