Use the discriminant to determine the number and type of solutions of the equation.
-$x ^ { 2 } + 5 x - 6 = 0$
A) one real solution
B) two complex but not real solutions
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, $a = 1$, $b = 5$, and $c = -6$, so the discriminant is $5^2 - 4(1)(-6) = 25 + 24 = 49$. Since the discriminant is positive, the equation has two real solutions.

Use the Discriminant to Determine the Number and Type of Solutions