Use the discriminant to determine the number and type of solutions of the equation.
-$$10 - 8 x ^ { 2 } = - 6 x + 9$$
A) Two complex but not real solutions
B) Two real solutions
C) One real solution

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. First, we rearrange the given equation to standard form: $8x^2 - 6x + (10 - 9) = 0$, which simplifies to $8x^2 - 6x + 1 = 0$. Here, $a = 8$, $b = -6$, and $c = 1$. The discriminant is $(-6)^2 - 4(8)(1) = 36 - 32 = 4$. Since the discriminant is positive, the equation has two real solutions.

Use the Discriminant to Determine the Number and Type of Solutions