Use the discriminant to determine the type and number of solutions. $$- 5 x ^ { 2 } + 5 x + 1 = 0$$
A) Two rational solutions
B) Two irrational solutions
C) One rational solution
D) Two imaginary 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 given equation, $a = -5$, $b = 5$, and $c = 1$, so $D = 5^2 - 4(-5)(1) = 25 + 20 = 45$. Since $D > 0$ and is not a perfect square, the equation has two irrational solutions.

Use the Discriminant to Determine the Type and Number of Solutions