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.
-$$t ^ { 2 } + 6 t + 9 = 0$$
A) Two distinct irrational solutions
B) Two distinct rational solutions
C) One rational solution (a double solution)
D) Two distinct nonreal complex 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 $t^2 + 6t + 9 = 0$, the discriminant is $6^2 - 4(1)(9) = 36 - 36 = 0$. A discriminant of 0 indicates that there is exactly one rational solution (a double solution), hence option C is correct.

Evaluate the Discriminant for the Equation t2+6t+9=0t ^ { 2 } + 6 t + 9 = 0t2+6t+9=0

Evaluate the Discriminant for the Equation $t ^ { 2 } + 6 t + 9 = 0$