Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the
equation.
-$$5 x ^ { 2 } - 3 x - 1 = 0$$
A)two nonreal solutions
B)exactly one real solution
C)two real 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, $a = 5$, $b = -3$, and $c = -1$, so the discriminant is $(-3)^2 - 4(5)(-1) = 9 + 20 = 29$. Since the discriminant is positive, the equation has two real solutions.

Use the Discriminant to Determine the Number and Nature of the Solutions