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.
-$$w ^ { 2 } - 2 w + 6 = 0$$
A) One rational solution (a double solution)
B) Two distinct rational solutions
C) Two distinct irrational solutions
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 $w^2 - 2w + 6 = 0$, the discriminant is $(-2)^2 - 4(1)(6) = 4 - 24 = -20$. Since the discriminant is negative, this means the equation has two distinct nonreal complex solutions.

Evaluate the Discriminant for the Equation w2−2w+6=0w ^ { 2 } - 2 w + 6 = 0w2−2w+6=0

Evaluate the Discriminant for the Equation $w ^ { 2 } - 2 w + 6 = 0$