Use the discriminant to determine the type and number of solutions.
-$$5 x ^ { 2 } + 4 x + 5 = 0$$
A) Two imaginary solutions
B) One rational solution
C) Two rational solutions
D) Two irrational 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, $a = 5$, $b = 4$, and $c = 5$, so the discriminant is $4^2 - 4(5)(5) = 16 - 100 = -84$. Since the discriminant is negative, the equation has two imaginary solutions.

Use the Discriminant to Determine the Type and Number of Solutions