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.
-$v ^ { 2 } - 5 v - 3 = 0$
A) Two distinct nonreal complex solutions
B) Two distinct irrational solutions
C) One rational solution (a double solution)
D) Two distinct rational solutions

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $D = b^2 - 4ac$. For the equation $v^2 - 5v - 3 = 0$, $a = 1$, $b = -5$, and $c = -3$, so the discriminant is $D = (-5)^2 - 4(1)(-3) = 25 + 12 = 37$. Since 37 is positive and not a perfect square, the equation has two distinct irrational solutions.

Evaluate the Discriminant for the Equation v2−5v−3=0v ^ { 2 } - 5 v - 3 = 0v2−5v−3=0

Evaluate the Discriminant for the Equation $v ^ { 2 } - 5 v - 3 = 0$