Use the discriminant to determine the type and number of solutions.
-$$- 2 x ^ { 2 } + 5 x + 5 = 0$$
A) One rational solution
B) Two rational solutions
C) Two irrational solutions
D) Two imaginary 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, $a = -2$, $b = 5$, and $c = 5$, so the discriminant is $5^2 - 4(-2)(5) = 25 + 40 = 65$. Since the discriminant is positive and not a perfect square, the equation has two irrational solutions.

Use the Discriminant to Determine the Type and Number of Solutions