Use the discriminant to determine the number and type of solutions of the equation.
-$5 - 4 x ^ { 2 } = - 6 x + 3$
A) two complex but not real solutions
B) one real solution
C) two real solutions

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. First, rearrange the given equation to standard form: $4x^2 + 6x + (5 - 3) = 0$, which simplifies to $4x^2 + 6x + 2 = 0$. Here, $a = 4$, $b = 6$, and $c = 2$. The discriminant is $6^2 - 4(4)(2) = 36 - 32 = 4$. Since the discriminant is positive, the equation has two real solutions.

Use the Discriminant to Determine the Number and Type of Solutions