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.
-$$s ^ { 2 } - 6 s + 5 = 0$$
A) One rational solution (a double solution)
B) Two distinct nonreal complex solutions
C) Two distinct irrational solutions
D) Two distinct rational solutions

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the given equation $s^2 - 6s + 5 = 0$, the discriminant is $(-6)^2 - 4(1)(5) = 36 - 20 = 16$. Since the discriminant is positive and a perfect square, the equation has two distinct rational solutions.

Evaluate the Discriminant for the Equation s2−6s+5=0s ^ { 2 } - 6 s + 5 = 0s2−6s+5=0

Evaluate the Discriminant for the Equation $s ^ { 2 } - 6 s + 5 = 0$