Use the discriminant to determine the type and number of solutions.
-$$6 q ^ { 2 } = 1$$
A) Two rational solutions
B) Two irrational solutions
C) Two imaginary solutions
D) One rational solutions

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation in the form $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the equation $6q^2 = 1$ or $6q^2 - 1 = 0$, we have $a = 6$, $b = 0$, and $c = -1$. Thus, the discriminant is $0^2 - 4(6)(-1) = 24$, which is positive, indicating two real solutions. Since the discriminant is not a perfect square, the solutions are irrational.

Use the Discriminant to Determine the Type and Number of Solutions