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.
-$w ^ { 2 } - 3 w + 8 = 0$
A) Two distinct rational solutions
B) Two distinct irrational 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 $w^2 - 3w + 8 = 0$, the discriminant is $(-3)^2 - 4(1)(8) = 9 - 32 = -23$. Since the discriminant is negative, the equation has two distinct nonreal complex solutions.

Evaluate the Discriminant for the Equation w2−3w+8=0w ^ { 2 } - 3 w + 8 = 0w2−3w+8=0

Evaluate the Discriminant for the Equation $w ^ { 2 } - 3 w + 8 = 0$