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.
-$$v ^ { 2 } - 7 v + 7 = 0$$
A) Two distinct irrational solutions
B) Two distinct nonreal complex 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 $v^2 - 7v + 7 = 0$, $a = 1$, $b = -7$, and $c = 7$. Thus, the discriminant is $(-7)^2 - 4(1)(7) = 49 - 28 = 21$. Since the discriminant is positive and not a perfect square, the equation has two distinct irrational solutions.

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

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