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.
-$s ^ { 2 } + 4 s + 3 = 0$
A) Two distinct nonreal complex solutions
B) Two distinct irrational solutions
C) Two distinct rational solutions
D) One rational solution (a double solution)

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 $s^2 + 4s + 3 = 0$, $a = 1$, $b = 4$, and $c = 3$, so the discriminant is $4^2 - 4(1)(3) = 16 - 12 = 4$. Since the discriminant is positive and a perfect square, there are two distinct rational solutions.

Evaluate the Discriminant for the Equation s2+4s+3=0s ^ { 2 } + 4 s + 3 = 0s2+4s+3=0

Evaluate the Discriminant for the Equation $s ^ { 2 } + 4 s + 3 = 0$