Compute the discriminant. Then determine the number and type of solutions for the given equation.
-$$6 x ^ { 2 } = - 8 x - 7$$
A) $- 104$; two complex imaginary solutions
B) 0 ; one real solution
C) 232 ; two unequal real solutions

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $D = b^2 - 4ac$. For the equation $6x^2 = -8x - 7$, rearranging gives $6x^2 + 8x + 7 = 0$, where $a = 6$, $b = 8$, and $c = 7$. Thus, $D = 8^2 - 4(6)(7) = 64 - 168 = -104$. A negative discriminant indicates two complex imaginary solutions.

Compute the Discriminant 6x2=−8x−76 x ^ { 2 } = - 8 x - 76x2=−8x−7

Compute the Discriminant $6 x ^ { 2 } = - 8 x - 7$