Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
-$t ^ { 2 } + 12 t + 36 = 0$
A) Two distinct irrational solutions
B) Two distinct nonreal complex solutions
C) One rational solution (a double solution)
D) Two distinct rational 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 $t^2 + 12t + 36 = 0$, $a = 1$, $b = 12$, and $c = 36$. Thus, the discriminant is $12^2 - 4(1)(36) = 144 - 144 = 0$. A discriminant of 0 indicates that there is exactly one rational solution, which is a double solution.

Evaluate the Discriminant for the Equation t2+12t+36=0t ^ { 2 } + 12 t + 36 = 0t2+12t+36=0

Evaluate the Discriminant for the Equation $t ^ { 2 } + 12 t + 36 = 0$