Use the discriminant to determine the number and type of solutions of the equation.
-$$5 + 4 x ^ { 2 } = - 7 x$$
A) Two real solutions
B) One real solution
C) Two complex but not real 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 $4x^2 + 7x + 5 = 0$, $a = 4$, $b = 7$, and $c = 5$, so the discriminant is $7^2 - 4(4)(5) = 49 - 80 = -31$. Since the discriminant is negative, the equation has two complex but not real solutions.

Use the Discriminant to Determine the Number and Type of Solutions