Without solving, determine the character of the solutions of the equation.
-$$x ^ { 2 } - 8 x + 16 = 0$$
A) a repeated real solution
B) two complex solutions that are conjugates of each other
C) two unequal real solutions

Question

Quizplus · Accepted Answer

The given equation is a quadratic equation of the form $ax^2 + bx + c = 0$, where $a = 1$, $b = -8$, and $c = 16$. The discriminant of a quadratic equation is given by $\Delta = b^2 - 4ac$. For this equation, $\Delta = (-8)^2 - 4(1)(16) = 64 - 64 = 0$. A discriminant of zero indicates that the equation has a repeated real solution, hence option A is correct.

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