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.
-$v ^ { 2 } - 4 v - 7 = 0$
A) One rational solution (a double solution)
B) Two distinct irrational solutions
C) Two distinct nonreal complex solutions
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 $v^2 - 4v - 7 = 0$, $a = 1$, $b = -4$, and $c = -7$, so the discriminant is $D = (-4)^2 - 4(1)(-7) = 16 + 28 = 44$. Since $D > 0$ and is not a perfect square, the equation has two distinct irrational solutions.

Evaluate the Discriminant for the Equation v2−4v−7=0v ^ { 2 } - 4 v - 7 = 0v2−4v−7=0

Evaluate the Discriminant for the Equation $v ^ { 2 } - 4 v - 7 = 0$