Without solving, determine the character of the solutions of the equation.
-$$x ^ { 2 } + 8 x - 5 = 0$$
A) two complex solutions that are conjugates of each other
B) a repeated real solution
C) two unequal real 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, $a = 1$, $b = 8$, and $c = -5$, so the discriminant is $D = 8^2 - 4(1)(-5) = 64 + 20 = 84$. Since $D > 0$, the equation has two unequal real solutions.

Without Solving, Determine the Character of the Solutions of the Equation